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The class of modules with projective cover

Yonghua Guo
대한수학회 (The Korean Mathematical Society)|2009.01|대한수학회지 (Journal of the KMS)|제46권 제1호|pp. 51-58

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참고문헌

키워드

perfect ringprojective coverC_{P}-hereditary ringsmall submodule
주제분류수학

초록

Let R be a ring. A right R-module M is called perfect if M possesses a projective cover. In this paper, we consider the relationship between the class of perfect modules and other classes of modules. Some known rings are characterized by these relationships.

Abstract

Let R be a ring. A right R-module M is called perfect if M possesses a projective cover. In this paper, we consider the relationship between the class of perfect modules and other classes of modules. Some known rings are characterized by these relationships.

참고문헌 (9)

  1. F. W. Anderson, "Rings and Categories of Modules, Second edition", Graduate Texts in Mathematics, 13 (1992), Springer-Verlag
  2. G. Azumaya, "Rings of pure global dimension zero and Mittag-Leffler modules", J. Pure Appl. Algebra, 62(2), pp.109~122 (1989)
  3. H. Bass, "Finitistic dimension and a homological generalization of semi-primary rings", Trans. Amer. Math. Soc., 95, pp.466~488 (1960)
  4. H. Cartan, "Homological Algebra" (1956), Princeton Univ. Press
  5. J. Clark, "Lifting Modules, Supplements and projectivity in module theory", Frontiers in Mathematics (2006), Verlag
  6. D. J. Fieldhouse, "Characterizations of modules", Canad. J. Math, 23, pp.608~610 (1971)
  7. T. H. Fay, "Relative injectivity", Chinese J. Math, 22(1), pp.65~94 (1994)
  8. K. R. Goodeal, "Ring Theory: Nonsingular Rings and Modules, Pure and Applied Math-ematics", Marcel Dekker, Inc., (33) (1976), New York-Basel
  9. P. A. Guil Asensio, "Sigma-cotorsion rings", Adv. Math, 191(1), pp.11~28 (2005)

관련 논문AI추천

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