In this paper, we study the relation between m-strongly Gorenstein projective (resp. injective) modules and n-strongly Gorenstein projective (resp. injective) modules whenever m 6= n, and the homological behavior of n-strongly Gorenstein projective (resp. injective) modules. We introduce the notion of n-strongly Gorenstein flat modules. Then we study the homological behavior of n-strongly Goren...

In this paper, we study a particular case of Gorenstein projective, injective, and flat modules, which we call, respectively, strongly Gorenstein projective, injective, and flat modules. These last three classes of modules give us a new characterization of the first modules, and confirm that there is an analogy between the notion of “Gorenstein projective, injective, and flat modules”and the no...

Abstract Let S be a domain and R = [ t ; σ, δ ] skew polynomial ring, where σ is an injective endomorphism of left -derivation. We give criteria for polynomials f ∈ degree less or equal to four irreducible. apply them low in quantized Weyl algebras the quantum planes. also consider ( ) m − .

By results of Löffler and Comezaña, the Pontrjagin-Thom map from geometric G-equivariant bordism to homotopy theoretic equivariant bordism is injective for compact abelian G. If G = S×. . .×S, we prove that the associated fixed point square is a pull back square, thus confirming a recent conjecture of Sinha [22]. This is used in order to determine the image of the Pontrjagin-Thom map for toral G.

Let τ be a hereditary torsion theory on the category R-Mod of left R-modules over an associative unitary ring R. We introduce the notion of τ-natural class as a class of modules closed under τ-dense submodules, direct sums, and τ-injective hulls. We study connections between certain conditions involving τ-(quasi-)injectivity in the context of τnatural classes, generalizing results established b...

We obtain some methods to construct a (strongly) proper resolution (resp. coproper coresolution) of one end term in a short exact sequence from that of the other two terms. By using this method, we prove that for a left and right Noetherian ring R, RR satisfies the Auslander condition if and only if so does every flat left R-module, if and only if the injective dimension of the ith term in a mi...

For a semigroup S we define some operations on the set of soft S-acts. Also by defining the soft congruence we introduce the notion of bi-act. The purpose of this paper is to investigate certain results on the soft bi-acts. Some analoges of algebraic properties like the isomorphisms theorems will be appeared as well.

We continue in this paper the study of positively ordered monoids (P.O.M.’s) initiated in [39]. We prove that injective P.O.M.’s are the retracts of the powers of P=[0, ∞]. We also characterize the natural P.O.M.homomorphism from a given refinement P.O.M to its bidual, with e.g. applications to decomposition spaces. As another application, we prove that a refinement P.O.M admits a ‘Banach limit...

The principle “Every result in classical homological algebra should have a counterpart in Gorenstein homological algebra” was given by Henrik Holm. There is a remarkable body of evidence supporting this claim. Perhaps one of the most glaring exceptions is provided by the fact that tensor products of Gorenstein projective modules need not be Gorenstein projective, even over Gorenstein rings. So ...