D3-Modules

A right R-module M is called a D3-module, if M 1 and M 2 are direct summands of M with M = M 1 + M 2, then M 1 ∩ M 2 is a direct summand of M. Following the work of Bass on projective covers, we introduce the notion of D3-covers and provide new characterizations of several well-known classes of rings in terms of D3-modules and D3-covers.

[1]  Katharina Weiss,et al.  Lectures On Modules And Rings , 2016 .

[2]  J. Golan.  CHARACTERIZATION OF RINGS USING QUASIPROJECTIVE MODULES. II , 2010 .

[3]  E. A. Rutter,et al.  GENERALIZATIONS OF QF-3 ALGEBRAS , 2010 .

[4]  S. Rizvi,et al.  On direct sums of Baer modules , 2009 .

[5]  馬場 良始,et al.  Classical artinian rings and related topics , 2009 .

[6]  A. Hamdouni,et al.  CHARACTERIZATION OF MODULES AND RINGS BY THE SUMMAND INTERSECTION PROPERTY AND THE SUMMAND SUM PROPERTY , 2005 .

[7]  M. Alkan,et al.  On Summand Sum and Summand Intersection Property of Modules , 2002 .

[8]  W. K. Nicholson,et al.  On Quasi-Frobenius Rings , 2003 .

[9]  E. Enochs,et al.  All Modules Have Flat Covers , 2001 .

[10]  D. Keskin.  On lifting modules , 2000 .

[11]  W. Xue,et al.  Rings Whose Modules Are ⊕ -Supplemented , 1999 .

[12]  John Dauns.  Modules and Rings , 1994 .

[13]  W. Xue.  Characterization of rings using direct-projective modules and direct-injective modules , 1993 .

[14]  Robert Wisbauer,et al.  Foundations of module and ring theory , 1991 .

[15]  Saad H. Mohamed,et al.  Continuous and Discrete Modules , 1990 .

[16]  J. García.  Properties of direct summands of modules , 1989 .

[17]  A. Schofield,et al.  On semihereditary rings , 1988 .

[18]  G. Wilson.  Modules with the summand intersection property , 1986 .

[19]  J. O'neill.  On direct products of modules , 1984 .

[20]  K. Oshiro.  Semiperfect modules and quasisemiperfect modules , 1983 .

[21]  E. Enochs.  Injective and flat covers, envelopes and resolvents , 1981 .

[22]  James Whitehead,et al.  PROJECTIVE MODULES , 2011 .

[23]  W. Vasconcelos,et al.  Coherence of polynomial rings , 1976 .

[24]  Frank W. Anderson,et al.  Rings and Categories of Modules , 1974 .

[25]  E. Walker,et al.  Direct-sum representations of injective modules , 1967 .

[26]  H. Bass.  Finitistic dimension and a homological generalization of semi-primary rings , 1960 .