논문KCI 등재
On reflexive modules over commutative rings
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Let $R$ be a commutative ring and $U$ an $R$-module. The aim of this paper is to study the duality between $U$-reflexive (pre)envelopes and $U$-reflexive (pre)covers of $R$-modules.
Abstract
Let $R$ be a commutative ring and $U$ an $R$-module. The aim of this paper is to study the duality between $U$-reflexive (pre)envelopes and $U$-reflexive (pre)covers of $R$-modules.
참고문헌 (26)
- F. W. Anderson, "Rings and Categories of Modules" (1992), Springer-Verlag
- M. Auslander, "Stable module theory", Memoirs of the American Mathematical Society, (94) (1969), American Mathematical Society
- R. G. Belshoff, "Matlis reflexive modules", Comm. Algebra, 19(4), pp.1099~1118 (1991)
- R. G. Belshoff, "Remarks on reflexive modules, covers, and envelopes", Beitr¨age Algebra Geom, 50(2), pp.353~362 (2009)
- R. G. Belshoff, "Generalized Matlis duality", Proc. Amer. Math. Soc, 128(5), pp.1307~1312 (2000)
- R. G. Belshoff, "Injective envelopes and flat covers of Matlis reflexive modules", J. Pure Appl. Algebra, 79(3), pp.205~215 (1992)
- W. Bruns, "Cohen-Macaulay Rings (revised edition)", Advances in Math, 39 (1996), Cambridge Univ. Press
- L. W. Christensen, "Gorenstein Dimension", Lecture Notes in Math, 1747 (2000), Springer-Verlag
- N. Q. Ding, "On envelopes with the unique mapping property", Comm. Algebra, 24(4), pp.1459~1470 (1996)
- E. E. Enochs, "Injective and flat covers, envelopes and resolvents", Israel J. Math, 39(3), pp.189~209 (1981)
- E. E. Enochs, "Compact coGalois groups", Math. Proc. Cambridge Philos. Soc, 128(2), pp.233~244 (2000)
- E. E. Enochs, "Covering morphisms", Comm. Algebra, 28(8), pp.3823~3835 (2000)
- E. E. Enochs, "Are covering (enveloping) morphisms minimal?", Proc. Amer. Math. Soc, 128(10), pp.2863~2868 (2000)
- E. E. Enochs, "Finitely generated cotorsion modules", Proc. Edinb. Math. Soc, 44(1), pp.143~152 (2001)
- E. E. Enochs, "Injective envelopes and (Gorenstein) flat covers", Algebr. Represent. Theory, 15(6), pp.1131~1145 (2012)
- E. E. Enochs, "Gorenstein injective and projective modules", Math. Z, 220(4), pp.611~633 (1995)
- E. E. Enochs, "Relative Homological Algebra" (2000), Walter de Gruyter
- E. E. Enochs, "A generalization of Auslander’s last theorem", Algebr. Represent. Theory, 2(3), pp.259~268 (1999)
- M. Hashimoto, "Some remarks on index and generalized Loewy length of a Gorenstein local ring", J. Algebra, 187(1), pp.150~162 (1997)
- H. Holm, "Gorenstein homological dimensions", J. Pure Appl. Algebra, 189(1-3), pp.167~193 (2004)
- Z. Y. Huang, "Proper resolutions and Gorenstein categories", J. Algebra, 393, pp.142~169 (2013)
- Z. Y. Huang, "Duality of preenvelopes and pure injective modules", Canad. Math. Bull, 57(2), pp.318~325 (2014)
- D. A. Jorgensen, "Independence of the total reflexivity conditions for modules", Algebr. Represent. Theory, 9(2), pp.217~226 (2006)
- W. V. Vasconcelos, "Reflexive modules over Gorenstein rings", Proc. Amer. Math. Soc, 19, pp.1349~1355 (1968)
- W. M. Xue, "Injective envelopes and flat covers of modules over a commutative ring", J. Pure Appl. Algebra, 109(2), pp.213~220 (1996)
- Y. Yoshino, "Cohen-Macaulay approximations", Proc. symposium on representation theory of algebras, pp.119~138 (1993)
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