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Volumn 47, Issue 4, 2002, Pages 443-477

Quotients of partial abelian monoids and the Riesz decomposition property

Author keywords

Congruence; Effect algebra; Ordered abelian group; Partial abelian monoid; Riesz decomposition property

Indexed keywords


EID: 0036433963     PISSN: 00025240     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00012-002-8199-7     Document Type: Article
Times cited : (29)

References (56)
  • 1
    • 0000443244 scopus 로고
    • Free sums of groups and their generalizations, An analysis of the associative law
    • R. Baer, Free sums of groups and their generalizations. An analysis of the associative law, Amer. J. Math. 41 (1949), 706-742.
    • (1949) Amer. J. Math. , vol.41 , pp. 706-742
    • Baer, R.1
  • 4
    • 0004211322 scopus 로고
    • Springer-Verlag, Berlin, Heidelberg, New York
    • Springer-Verlag, Berlin, Heidelberg, New York, 1972.
    • (1972) Baer*-Rings
    • Berberian, S.K.1
  • 7
    • 84966215015 scopus 로고
    • Inductive limits of finite-dimensional C*-algebras
    • O. Bratteli, Inductive limits of finite-dimensional C*-algebras, Trans. Amer. Math. Soc. 171 (1972), 195-234.
    • (1972) Trans. Amer. Math. Soc. , vol.171 , pp. 195-234
    • Bratteli, O.1
  • 12
    • 84968495744 scopus 로고
    • Algebraic analysis of many-valued logic
    • C.C. Chang, Algebraic analysis of many-valued logic, Trans. Amer. Math. Soc. 88 (1958), 467-490.
    • (1958) Trans. Amer. Math. Soc. , vol.88 , pp. 467-490
    • Chang, C.C.1
  • 13
    • 0043190394 scopus 로고    scopus 로고
    • Some ideal lattices in partial abelian monoids and effect algebras
    • G. Chevalier and S. Pulmannová, Some ideal lattices in partial abelian monoids and effect algebras, Order 17 (2000),75-92.
    • (2000) Order , vol.17 , pp. 75-92
    • Chevalier, G.1    Pulmannová, S.2
  • 14
    • 0000268612 scopus 로고
    • Dimension groups and their affine representation
    • E.G. Efross, D.E. Handelmann, and C.L. Shen, Dimension groups and their affine representation, Amer. J. Math. 102 (1980), 385-407.
    • (1980) Amer. J. Math. , vol.102 , pp. 385-407
    • Efross, E.G.1    Handelmann, D.E.2    Shen, C.L.3
  • 15
    • 0003092457 scopus 로고
    • On the classification of inductive limits of equences of semisimple finite-dimensional algebras
    • G.A. Elliott, On the classification of inductive limits of equences of semisimple finite-dimensional algebras, J. Algebra 38 (1979), 29-44.
    • (1979) J. Algebra , vol.38 , pp. 29-44
    • Elliott, G.A.1
  • 20
    • 0003265876 scopus 로고
    • Partially ordered groups with interpolation
    • Amer. Math. Soc., Providence, Rhode Island
    • K.R. Goodearl, Partially Ordered Groups with Interpolation, Math. Surveys and Monographs No. 20, Amer. Math. Soc., Providence, Rhode Island, 1986.
    • (1986) Math. Surveys and Monographs , vol.20
    • Goodearl, K.R.1
  • 23
    • 0003119024 scopus 로고
    • The center of an effect algebra
    • R. Greechie, D. Foulis, and S. Pulmannová, The center of an effect algebra, Order 12 (1995), 91-106.
    • (1995) Order , vol.12 , pp. 91-106
    • Greechie, R.1    Foulis, D.2    Pulmannová, S.3
  • 24
    • 0004014114 scopus 로고
    • Academic Press Inc., Boston, San Diego, New York, Berkley, Tokyo, Toronto
    • S.P. Gudder, Quantum Probability, Academic Press Inc., Boston, San Diego, New York, Berkley, Tokyo, Toronto, 1988.
    • (1988) Quantum Probability
    • Gudder, S.P.1
  • 25
    • 0030537493 scopus 로고    scopus 로고
    • Lattice properties of quantum effects
    • S.P. Gudder, Lattice properties of quantum effects, J. Math. Phys. 37 (1996), 2637-2642.
    • (1996) J. Math. Phys. , vol.37 , pp. 2637-2642
    • Gudder, S.P.1
  • 26
    • 0031473107 scopus 로고    scopus 로고
    • Quotients of partial abelian monoids
    • S.P. Gudder and S.J. Pulmannová, Quotients of partial abelian monoids, Algebra univers. 38 (1998), 395-421.
    • (1998) Algebra univers. , vol.38 , pp. 395-421
    • Gudder, S.P.1    Pulmannová, S.J.2
  • 28
    • 84968500032 scopus 로고
    • An m-orthocomplete orthomodular lattice in m-complete
    • S. Holland, Jr., An m-orthocomplete orthomodular lattice in m-complete, Proc. Amer. Math. Soc. 24 (1970), 716-718.
    • (1970) Proc. Amer. Math. Soc. , vol.24 , pp. 716-718
    • Holland S., Jr.1
  • 29
    • 0002002333 scopus 로고
    • On axiom systems of propositional calculi
    • Y. Imai and K. Iséki, On axiom systems of propositional calculi, Proc. Japan Acad. 42 (1966), 19-22.
    • (1966) Proc. Japan Acad. , vol.42 , pp. 19-22
    • Imai, Y.1    Iséki, K.2
  • 30
    • 0011577106 scopus 로고
    • A note on generalized orthomodular lattices
    • M.F. Janowitz, A note on generalized orthomodular lattices, J. Natur. Sci. Math. 8 (1968), 89-94.
    • (1968) J. Natur. Sci. Math. , vol.8 , pp. 89-94
    • Janowitz, M.F.1
  • 34
    • 0000945404 scopus 로고
    • An axiomatization for abelian relative inverses
    • G. Kalmbach and Z. Riečanová, An axiomatization for abelian relative inverses, Dem. Math. 27 (1994) 684-699.
    • (1994) Dem. Math. , vol.27 , pp. 684-699
    • Kalmbach, G.1    Riečanová, Z.2
  • 36
    • 0011577587 scopus 로고
    • Rossijskij gosudarstvennyj pedagogičeskij universitet imeni A.I. Gercena, Izdatelstvo "Obrazovanie", St. Petersburg
    • E.S. Ljapin and A.E. Evseev, Partial algebraic operations (Russian), Rossijskij gosudarstvennyj pedagogičeskij universitet imeni A.I. Gercena, Izdatelstvo "Obrazovanie", St. Petersburg, 1991.
    • (1991) Partial algebraic operations (Russian)
    • Ljapin, E.S.1    Evseev, A.E.2
  • 37
    • 0011628696 scopus 로고
    • The lattice theoretic background of the dimension theory of operator algebras
    • L.H. Loomis, The lattice theoretic background of the dimension theory of operator algebras, Mem. Amer. Math. Soc. 1955 (1955), no. 18.
    • (1955) Mem. Amer. Math. Soc. , vol.1955 , Issue.18
    • Loomis, L.H.1
  • 38
    • 0011577863 scopus 로고
    • Dimension functions on certain general lattices
    • S. Maeda, Dimension functions on certain general lattices, J. Sci. Hiroshima Univ. 19 (1955), 211-237.
    • (1955) J. Sci. Hiroshima Univ. , vol.19 , pp. 211-237
    • Maeda, S.1
  • 39
    • 0011693641 scopus 로고
    • On the lattice of projections of a baer*-ring
    • S. Maeda, On the lattice of projections of a Baer*-ring, J. Sci. Hiroshima Univ. 22 (1958), 75-88.
    • (1958) J. Sci. Hiroshima Univ. , vol.22 , pp. 75-88
    • Maeda, S.1
  • 41
    • 0000443669 scopus 로고
    • Generalized orthomodular posers
    • A. Mayet-Ippolito, Generalized orthomodular posers, Demonstratio Math. 24 (1991), 263-274.
    • (1991) Demonstratio Math. , vol.24 , pp. 263-274
    • Mayet-Ippolito, A.1
  • 42
    • 0001797805 scopus 로고
    • Interpretations of AF C*-algebras in Lukasziewicz sentential calculus
    • D. Mundici, Interpretations of AF C*-algebras in Lukasziewicz sentential calculus, J. Funct. Anal. 65 (1986), 15-63.
    • (1986) J. Funct. Anal. , vol.65 , pp. 15-63
    • Mundici, D.1
  • 43
    • 0001494367 scopus 로고
    • MV-algebras are categorically equivalent to bounded commutative BCK-algebras
    • D. Mundici, MV-algebras are categorically equivalent to bounded commutative BCK-algebras, Math. Japonica 6 (1986), 889-894.
    • (1986) Math. Japonica , vol.6 , pp. 889-894
    • Mundici, D.1
  • 44
    • 0000046768 scopus 로고
    • Extending addition in Elliott's local semigroup
    • D. Mundici and G. Panti, Extending addition in Elliott's local semigroup, J. Funct. Anal. 171 (1993), 461-472.
    • (1993) J. Funct. Anal. , vol.171 , pp. 461-472
    • Mundici, D.1    Panti, G.2
  • 46
    • 0001538723 scopus 로고    scopus 로고
    • Congruences in partial abelian semigroups
    • S. Pulmannová, Congruences in partial abelian semigroups, Algebra univers. 37 (1997), 119-140.
    • (1997) Algebra univers. , vol.37 , pp. 119-140
    • Pulmannová, S.1
  • 47
    • 0000456072 scopus 로고    scopus 로고
    • On connections among some orthomodular structures
    • S. Pulmannová, On connections among some orthomodular structures, Demonstratio Math. 30 (1997), 313-328.
    • (1997) Demonstratio Math. , vol.30 , pp. 313-328
    • Pulmannová, S.1
  • 50
    • 0011638258 scopus 로고
    • On commutative BCK-algebras
    • A. Romanowska and T. Traczyk, On commutative BCK-algebras, Math. Japonica 25 (1980), 567-583.
    • (1980) Math. Japonica , vol.25 , pp. 567-583
    • Romanowska, A.1    Traczyk, T.2
  • 51
    • 0040140765 scopus 로고
    • Ucebnyje zapisky Kazanskogo universiteta
    • A.N. Scherstnev, On boolean logics (Russian), Ucebnyje zapisky Kazanskogo universiteta. No 2 (1968), 48-62.
    • (1968) On boolean logics (Russian) , vol.2 , pp. 48-62
    • Scherstnev, A.N.1
  • 52
    • 0011638699 scopus 로고
    • A common abstraction of boolean rings and lattice ordered groups
    • K.D. Schmidt, A common abstraction of boolean rings and lattice ordered groups, Compositio Math. 54 (1985), 52-62.
    • (1985) Compositio Math. , vol.54 , pp. 52-62
    • Schmidt, K.D.1
  • 56
    • 0011689811 scopus 로고
    • The class of commutative BCK-algebrs is equationally definable
    • H. Yutani, The class of commutative BCK-algebrs is equationally definable, Math. Sem. Notes Kobe Univ. 5 (1977), 207-210.
    • (1977) Math. Sem. Notes Kobe Univ. , vol.5 , pp. 207-210
    • Yutani, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.