메뉴 건너뛰기




Volumn 190, Issue 2, 1997, Pages 280-328

Varieties of commutative residuated integral pomonoids and their residuation subreducts

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0031569723     PISSN: 00218693     EISSN: None     Source Type: Journal    
DOI: 10.1006/jabr.1996.6834     Document Type: Article
Times cited : (57)

References (62)
  • 2
    • 0001689776 scopus 로고
    • Equationally complete classes of commutative monoids with monus
    • [Ame84] K. Amer, Equationally complete classes of commutative monoids with monus, Algebra Universalis 18 (1984), 129-131.
    • (1984) Algebra Universalis , vol.18 , pp. 129-131
    • Amer, K.1
  • 3
    • 0003356656 scopus 로고
    • Lattice theory
    • Colloquium Publications, 3rd ed., reprinted with corrections, Providence RI
    • [Bir84] G. Birkhoff, "Lattice Theory," Colloquium Publications, Vol. 25, 3rd ed., reprinted with corrections, Am. Math. Soc., Providence RI, 1984.
    • (1984) Am. Math. Soc. , vol.25
    • Birkhoff, G.1
  • 4
    • 0000518612 scopus 로고
    • Hoops and their implicational reducts
    • Banach Center Publications, Institute of Mathematics, Polish Academy of Sciences, Warsaw
    • [BF93] W. J. Blok and I. M. A. Ferreirim, Hoops and their implicational reducts (Abstract), in " Algebraic Methods in Logic and in Computer Science," Banach Center Publications, Vol. 28, Institute of Mathematics, Polish Academy of Sciences, Warsaw, 1993.
    • (1993) Algebraic Methods in Logic and in Computer Science , vol.28
    • Blok, W.J.1    Ferreirim, I.M.A.2
  • 6
    • 0000030599 scopus 로고
    • On the structure of varieties with equationally definable principal congruences II
    • [BKP84] W. J. Blok, P. Köhler, and D. Pigozzi, On the structure of varieties with equationally definable principal congruences II, Algebra Universalis 18 (1984), 334-379.
    • (1984) Algebra Universalis , vol.18 , pp. 334-379
    • Blok, W.J.1    Köhler, P.2    Pigozzi, D.3
  • 7
    • 51249186512 scopus 로고
    • On the structure of varieties with equationally definable principal congruences I
    • [BP82] W. J. Blok and D. Pigozzi, On the structure of varieties with equationally definable principal congruences I, Algebra Universalis 15 (1982), 195-227.
    • (1982) Algebra Universalis , vol.15 , pp. 195-227
    • Blok, W.J.1    Pigozzi, D.2
  • 10
    • 0001089132 scopus 로고
    • On the structure of varieties with equationally definable principal congruences III
    • [BP94] W. J. Blok and D. Pigozzi, On the structure of varieties with equationally definable principal congruences III, Algebra Universalis 32 (1994), 545-608.
    • (1994) Algebra Universalis , vol.32 , pp. 545-608
    • Blok, W.J.1    Pigozzi, D.2
  • 11
    • 0010987901 scopus 로고
    • Failure of the congruence extension property in BCK-algebras and related structures
    • [BR93] W. J. Blok and J. G. Raftery, Failure of the congruence extension property in BCK-algebras and related structures, Math. Japonica 38 (1993), 633-638.
    • (1993) Math. Japonica , vol.38 , pp. 633-638
    • Blok, W.J.1    Raftery, J.G.2
  • 12
    • 0003074893 scopus 로고
    • On the quasivariety of BCK-algebras and its subvarieties
    • [BR95] W. J. Blok and J. G. Raftery, On the quasivariety of BCK-algebras and its subvarieties, Algebra Universalis 33 (1995), 68-90.
    • (1995) Algebra Universalis , vol.33 , pp. 68-90
    • Blok, W.J.1    Raftery, J.G.2
  • 13
    • 0000536614 scopus 로고
    • Komplementäre halbgruppen. Axiomatik und arithmetik
    • [Bos69] B. Bosbach, Komplementäre Halbgruppen. Axiomatik und Arithmetik, Fund. Math. 64 (1969), 257-287.
    • (1969) Fund. Math. , vol.64 , pp. 257-287
    • Bosbach, B.1
  • 15
    • 51249184177 scopus 로고
    • Distributivity and modularity of lattices of tolerance relations
    • [Cha81] I. Chajda, Distributivity and modularity of lattices of tolerance relations, Algebra Universalis 12 (1981), 247-255.
    • (1981) Algebra Universalis , vol.12 , pp. 247-255
    • Chajda, I.1
  • 16
    • 0010956473 scopus 로고
    • Tolerances in congruence permutable algebras
    • [Cha88] I. Chajda, Tolerances in congruence permutable algebras, Czechoslovak Math. J. 38 (1988), 218-225.
    • (1988) Czechoslovak Math. J. , vol.38 , pp. 218-225
    • Chajda, I.1
  • 17
    • 84968495744 scopus 로고
    • Algebraic analysis of many valued logics
    • [Cha58] C. C. Chang, Algebraic analysis of many valued logics, Trans. Amer. Math. Soc. 88 (1958), 467-490.
    • (1958) Trans. Amer. Math. Soc. , vol.88 , pp. 467-490
    • Chang, C.C.1
  • 18
    • 0001062490 scopus 로고
    • A large variety of BCK-algebras
    • [Cor81] W. H. Cornish, A large variety of BCK-algebras, Math. Japonica 26 (1981), 339-344.
    • (1981) Math. Japonica , vol.26 , pp. 339-344
    • Cornish, W.H.1
  • 20
    • 0011043287 scopus 로고
    • BCK-algebras with a supremum
    • [Cor82b] W. H. Cornish, BCK-algebras with a supremum, Math. Japonica 27 (1982), 63-73.
    • (1982) Math. Japonica , vol.27 , pp. 63-73
    • Cornish, W.H.1
  • 21
    • 0010957032 scopus 로고
    • BCK-algebras with a supremum II. Distributivity and interpolation
    • [Cor84] W. H. Cornish, BCK-algebras with a supremum II. Distributivity and interpolation, Math. Japonica 29 (1984), 439-447.
    • (1984) Math. Japonica , vol.29 , pp. 439-447
    • Cornish, W.H.1
  • 23
    • 0010992901 scopus 로고
    • n, n ≥ 2, is locally finite
    • n, n ≥ 2, is locally finite, Demonstratio Math. 20 (1987), 215-219.
    • (1987) Demonstratio Math. , vol.20 , pp. 215-219
    • Dyrda, K.1
  • 24
    • 84963062182 scopus 로고
    • Some connections between residual finiteness, finite embeddability and the word problem
    • [Eva69] T. Evans, Some connections between residual finiteness, finite embeddability and the word problem, J. London Math. Soc. 1 (1969), 399-403.
    • (1969) J. London Math. Soc. , vol.1 , pp. 399-403
    • Evans, T.1
  • 26
    • 38249028825 scopus 로고
    • Every BCK-algebra is a set of residuables in an integral pomonoid
    • [Fle88] I. Fleischer, Every BCK-algebra is a set of residuables in an integral pomonoid, J. Algebra 119 (1988), 360-365.
    • (1988) J. Algebra , vol.119 , pp. 360-365
    • Fleischer, I.1
  • 29
    • 0000891844 scopus 로고
    • A concrete ideal multiplication for algebraic systems and its relation to congruence distributivity
    • [HH79] J. Hagemann and C. Herrmann, A concrete ideal multiplication for algebraic systems and its relation to congruence distributivity, Arch. Math. (Basel) 32 (1979), 234-245.
    • (1979) Arch. Math. (Basel) , vol.32 , pp. 234-245
    • Hagemann, J.1    Herrmann, C.2
  • 30
    • 0003013265 scopus 로고
    • Dually residuated commutative monoids with identity element as least element do not form an equational class
    • [Hig84] D. Higgs, Dually residuated commutative monoids with identity element as least element do not form an equational class, Math. Japonica 29 (1984), 69-75.
    • (1984) Math. Japonica , vol.29 , pp. 69-75
    • Higgs, D.1
  • 31
    • 0000230931 scopus 로고
    • On varieties of BCK-algebras
    • [Idz83] P. M. Idziak, On varieties of BCK-algebras, Math. Japonica 28 (1983), 157-162.
    • (1983) Math. Japonica , vol.28 , pp. 157-162
    • Idziak, P.M.1
  • 32
    • 0000984431 scopus 로고
    • An algebra related with a propositional calculus
    • [Isé66] K. Iséki, An algebra related with a propositional calculus, Proc. Japan Acad. 42 (1966), 26-29.
    • (1966) Proc. Japan Acad. , vol.42 , pp. 26-29
    • Iséki, K.1
  • 33
    • 0010956474 scopus 로고
    • BCK-algebras with condition (S)
    • [Isé79] K. Iséki, BCK-algebras with condition (S), Math. Japonica 24 (1979), 107-119.
    • (1979) Math. Japonica , vol.24 , pp. 107-119
    • Iséki, K.1
  • 34
    • 0010953520 scopus 로고
    • On BCK-algebras with condition (S)
    • [Isé80] K. Iséki, On BCK-algebras with condition (S), Math. Japonica 24 (1980), 625-626.
    • (1980) Math. Japonica , vol.24 , pp. 625-626
    • Iséki, K.1
  • 35
    • 0002665895 scopus 로고
    • An introduction to the theory of BCK-algebras
    • [IT78] K. Iséki and S. Tanaka, An introduction to the theory of BCK-algebras, Math. Japonica 23 (1978), 1-26.
    • (1978) Math. Japonica , vol.23 , pp. 1-26
    • Iséki, K.1    Tanaka, S.2
  • 36
    • 0011003675 scopus 로고
    • Equational completeness and families of sets closed under subtraction
    • [Ka160] J. A. Kalman, Equational completeness and families of sets closed under subtraction, Nederl. Acad. Wetensch. Proc. Ser. A 63 (1960), 402-406.
    • (1960) Nederl. Acad. Wetensch. Proc. Ser. A , vol.63 , pp. 402-406
    • Kalman, J.A.1
  • 37
    • 38249002754 scopus 로고
    • Congruence permutable and congruence 3-permutable locally finite varieties
    • [Kea93] K. Kearnes, Congruence permutable and congruence 3-permutable locally finite varieties, J. Algebra 156 (1993), 36-49.
    • (1993) J. Algebra , vol.156 , pp. 36-49
    • Kearnes, K.1
  • 38
    • 84968466253 scopus 로고
    • Brouwerian semilattices
    • [Köh81] P. Köhler, Brouwerian semilattices, Trans. Amer. Math. Soc. 268 (1981), 103-126.
    • (1981) Trans. Amer. Math. Soc. , vol.268 , pp. 103-126
    • Köhler, P.1
  • 41
    • 0001751070 scopus 로고
    • Implication algebras are 3-permutable and 3-distributive
    • [Mit71] A. Mitschke, Implication algebras are 3-permutable and 3-distributive, Algebra Universalis 1 (1971), 182-186.
    • (1971) Algebra Universalis , vol.1 , pp. 182-186
    • Mitschke, A.1
  • 43
    • 0001494367 scopus 로고
    • MV-algebras are categorically equivalent to bounded commutative BCK-algebras
    • [Mun86] D. Mundici, MV-algebras are categorically equivalent to bounded commutative BCK-algebras, Math. Japonica 31 (1986), 889-894.
    • (1986) Math. Japonica , vol.31 , pp. 889-894
    • Mundici, D.1
  • 44
    • 0001984558 scopus 로고
    • Logics without the contraction rule
    • [OK85] H. Ono and Y. Komori, Logics without the contraction rule, J. Symbolic Logic 50 (1985), 169-201.
    • (1985) J. Symbolic Logic , vol.50 , pp. 169-201
    • Ono, H.1    Komori, Y.2
  • 47
    • 0000699110 scopus 로고
    • On ideal and congruence lattices of BCK-algebras
    • [Pał81] M. Pałasinski, On ideal and congruence lattices of BCK-algebras, Math. Japonica 26 (1981), 543-544.
    • (1981) Math. Japonica , vol.26 , pp. 543-544
    • Pałasinski, M.1
  • 48
    • 0000451263 scopus 로고
    • An embedding theorem for BCK-algebras
    • [Pał82] M. Pałasinski, An embedding theorem for BCK-algebras, Math. Seminar Notes Kobe Univ. 10 (1982), 749-751.
    • (1982) Math. Seminar Notes Kobe Univ. , vol.10 , pp. 749-751
    • Pałasinski, M.1
  • 51
    • 0011047347 scopus 로고
    • On a certain class of BCK-algebras with condition (S)
    • [Pon86] B. Pondělíček, On a certain class of BCK-algebras with condition (S), Math. Japonica 31 (1986), 775-782.
    • (1986) Math. Japonica , vol.31 , pp. 775-782
    • Pondělíček, B.1
  • 52
  • 53
    • 0011037655 scopus 로고
    • Tolerance numbers, congruence n-permutability and BCK-algebras
    • [RS92] J. G. Raftery and T. Sturm, Tolerance numbers, congruence n-permutability and BCK-algebras, Czechoslovak Math. J. 42 (1992), 727-740.
    • (1992) Czechoslovak Math. J. , vol.42 , pp. 727-740
    • Raftery, J.G.1    Sturm, T.2
  • 54
    • 0011029498 scopus 로고
    • On commutative BCK-algebras embeddable into directed commutative BCK-algebras
    • [Stu82] T. Sturm, On commutative BCK-algebras embeddable into directed commutative BCK-algebras, Math. Japonica 27 (1982), 197-212.
    • (1982) Math. Japonica , vol.27 , pp. 197-212
    • Sturm, T.1
  • 55
    • 85030011978 scopus 로고    scopus 로고
    • personal communication
    • [Stu] T. Sturm, personal communication.
    • Sturm, T.1
  • 57
    • 0000878208 scopus 로고
    • On the variety of bounded commutative BCK-algebras
    • [Tra79] T. Traczyk, On the variety of bounded commutative BCK-algebras, Math. Japonica 24 (1979), 283-292.
    • (1979) Math. Japonica , vol.24 , pp. 283-292
    • Traczyk, T.1
  • 58
    • 0010987256 scopus 로고
    • On the structure of BCK-algebras with zx · yx = zy · xy
    • [Tra88] T. Traczyk, On the structure of BCK-algebras with zx · yx = zy · xy, Math. Japonica 33 (1988), 319-324.
    • (1988) Math. Japonica , vol.33 , pp. 319-324
    • Traczyk, T.1
  • 60
    • 0002012003 scopus 로고
    • BCK-algebras do not form a variety
    • [Wro83] A. Wroński, BCK-algebras do not form a variety, Math. Japonica 28 (1983), 211-213.
    • (1983) Math. Japonica , vol.28 , pp. 211-213
    • Wroński, A.1
  • 61
    • 0000868541 scopus 로고
    • An algebraic motivation for BCK-algebras
    • [Wro85] A. Wroński, An algebraic motivation for BCK-algebras, Math. Japonica 30 (1985), 187-193.
    • (1985) Math. Japonica , vol.30 , pp. 187-193
    • Wroński, A.1
  • 62
    • 0000983819 scopus 로고
    • There is no largest variety of BCK-algebras
    • [WK84] A. Wroński and J. K. Kabziński, There is no largest variety of BCK-algebras, Math. Japonica 29 (1984), 545-549.
    • (1984) Math. Japonica , vol.29 , pp. 545-549
    • Wroński, A.1    Kabziński, J.K.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.