Let S be a class of left R-modules. An R-module M is said to be S-pure injective (resp. S-pure projective) if M has the injective (resp. projective) property respect to each S-pure exact sequence. Also, an R-module M is said to be S-pure flat if M has the flat property respect to each S-pure exact sequence. As Puninski (1994), let us fix a few of the most common purities S of R-modules.
Related Papers:
1- M. Behboodi
A generalization of the classical Krull dimension for modules
J. Algebra 305 (2006), 1128-1148
Related Papers:
1-M. Behboodi (Joint with R. Beyranvand)
Strong zero-divisor graphs of non-commutative rings
International Journal of Algebra 2 (2008), 25-44.
Papers:
1- M. Behboodi (Joint with Z. Rakeei)
The annihilating-ideal graph of commutative rings I
J. Algebra Appl. 10 (2011), 727-739
All our rings are associative rings with identity and modules are left (right) unital.
The question of which commutative rings have the property that every finitely generated module is a direct sum of cyclic modules has been around for many years. We will call these rings FGC-rings. The problem originated in I. Kaplanskys papers [5], [6];in which it was shown that a local domain is FGC if and only if it is an almost maximal valuation ring. For several years, this is one of the major open problems in the theory. The problem studied and solved in 1970s by various authors (R. S. Pierce[7], Brandal [2], Shores-R. Wiegand [8], S. Wiegand [10], Brandal-R.
Papers:
1-M. Behboodi
A generalization of Baer's lower nilradical for modules
J. Algebra Appl. 6 (2007), 337-353