Let R be a ring and n a fixed positive integer, we investigate the properties of n-strongly Gorenstein projective, injective and flat modules. Using the homological theory , we prove that the tensor product of an n-strongly Gorenstein projective (flat) right R -module and projective (flat) left R-module is also n-strongly Gorenstein projective (flat). Let R be a coherent ring ,we prove that the...

The author and Nakano recently proved that multiplicities in a Specht filtration of a symmetric group module are well-defined precisely when the characteristic is at least five. This result suggested the possibility of a symmetric group theory analogous to that of good filtrations and tilting modules for GLn(k). This paper is an initial attempt at such a theory. We obtain two sufficient conditi...

This paper generalize the idea of the authors in J. Pure Appl. Algebra 210 (2007) 437–445. Namely, we define and study a particular case of Gorenstein projective modules. We investigate some change of rings results for this new kind of modules. Examples over not necessarily Noetherian rings are given.

A class TC(X) of X-graphs is introduced, and an algorithmic property of labellings of nite strongly connected graphs by rational languages is shown to be decidable. This property, named as TC-inevitability, is a language-theoretic analogue of the R-inevitability of labellings of nite strongly connected graphs by nite monoids. As a consequence, the pseudovariety R of all nite R-trivial monoids i...

We consider transformations preserving certain linear structure in Grassmannians and give some generalization of the Fundamental Theorem of Projective Geometry and the Chow Theorem [Ch]. It will be exploited to study linear (k, n − k)-involutions, 1 < k < n − 1. The analogy of the J. Dieudonné and C. E. Rickart result will be obtained.

‎Let $R$ be a domain with quotiont field $K$‎, ‎and‎ ‎let $N$ be a submodule of an $R$-module $M$‎. ‎We say that $N$ is‎ ‎powerful (strongly primary) if $x,yin K$ and‎ ‎$xyMsubseteq N$‎, ‎then $xin R$ or $yin R$ ($xMsubseteq N$‎ ‎or $y^nMsubseteq N$ for some $ngeq1$)‎. ‎We show that a submodule‎ ‎with either of these properties is comparable to every prime‎ ‎submodule of $M$‎, ‎also we show tha...

We enrich the setting of strongly stable ideals (SSI): introduce shift modules, a module category encompassing SSIs. The recently introduced duality on SSIs is given an effective conceptual and computational setting. study in infinite dimensional polynomial rings, where most natural. Finally new type resolution for introduced. This projective modules.