Exchange property and the natural preorder between simple modules over semi-Artinian rings

Journal of Algebra

Volumn 253, Issue 1, 2002, Pages 133-166

  Baccella, Giuseppe ^a  

^a UNIVERSITY OF L'AQUILA   (Italy)

Author keywords

Artinian rings; Exchange rings; Idempotent ideals; Incidence algebras of posets; Perfect rings; Piecewise domains; Projective modules; Semi Artinian rings and modules; Semihereditary rings

Indexed keywords

EID: 0036660445     PISSN: 00218693     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0021-8693(02)00044-3     Document Type: Article

References (25)

1. F.W. Anderson, K.R. Fuller, Rings and Categories of Modules, Springer-Verlag, Berlin, 1974.
2. P. Ara, Extensions of exchange rings, J. Algebra 197 (1997) 409-423.
3. P. Ara, K.R. Goodearl, K.C. O'Meara, E. Pardo, Separative cancellation for projective modules over exchange rings, Israel J. Math. 105 (1998) 105-137.
4. M. Auslander, M.I. Platzeck, G. Todorov, Homological theory of idempotent ideals, Trans. Amer. Math. Soc. 332 (1992) 667-692.
5. G. Baccella, On C-semisimple rings. A study of the socle of a ring, Comm. Algebra 8 (1980) 889-909.
6. G. Baccella, Weakly semiprime rings, Comm. Algebra 12 (1984) 489-509.
7. G. Baccella, The structure of QF-3 rings with zero singular ideal, Comm. Algebra 15 (1987) 1393-1446.
8. G. Baccella, Semi-Artinian V -rings and semi-Artinian Von Neumann regular rings, J. Algebra 173 (1995) 587-612.
9. G. Baccella, G. Di Campli, Semi-Artinian rings whose Loewy factors are nonsingular, Comm. Algebra 25 (1997) 2743-2764.
10. G. Brookfield, Monoids and categories of Noetherian modules, PhD dissertation, University of California, Santa Barbara, 1997.
11. W.D. Burgess, K.R. Fuller, On quasihereditary rings, Proc. Amer. Math. Soc. 106 (1989) 321-328.
12. V.P. Camillo, K.R. Fuller, On Loewy length of rings, Pacific J. Math. 53 (1974) 347-354.
13. V.P. Camillo, K.R. Fuller, A note on Loewy rings and chain conditions on primitive ideals, in: Module Theory, Proc. Special Session, Amer. Math. Soc., Univ. Washington, Seattle, WA, 1977, in: Lecture Notes in Math., Vol. 700, Springer-Verlag, Berlin, 1979, pp. 75-86.
14. V. Dlab, C.M. Ringel, Quasi-hereditary algebras, Illinois J. Math. 33 (1989) 280-291.
15. N.V. Dung, P.F. Smith, On Semi-Artinian V -modules, J. Pure Appl. Algebra 82 (1) (1992) 27-37.
16. L. Fuchs, Torsion preradicals and ascending Loewy series of modules, J. Reine Angew. Math. Wiss. 239/240 (1969) 169-179.
17. R. Gordon, Classical quotient rings of PWD's, Proc. Amer. Math. Soc. 36 (1972) 39-46.
18. R. Gordon, L.W. Small, Piecewise domains, J. Algebra 23 (1972) 553-564.
19. G. Higman, Ordering by divisibility in abstract algebras, Proc London Math. Soc. (3) 2 (1952) 326-336.
20. G. Michler, Idempotent ideals in perfect rings, Canad. J. Math. 21 (1969) 301-309.
21. W.K. Nicholson, Lifting idempotents and exchange rings, Trans. Amer. Math. Soc. 229 (1977) 269-279.
22. B.L. Osofsky, Loewy length of perfect rings, Proc. Amer. Math. Soc. 28 (1971) 352-354.
23. D. Simson, Vector spaces categories, right peak rings and their socle projective modules, J. Algebra 92 (1985) 532-571.
24. D. Simson, Linear Representations of Partially Ordered Sets and Vector Space Categories, Gordon and Breach, Berlin, 1992.
25. R.B. Warfield Jr., Exchange rings and decompositions of modules, Math. Ann. 199 (1972) 31-36.