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...

Let Λ be an Artinian algebra and F an additive subbifunctor of ExtΛ(−,−) having enough projectives and injectives. We prove that the dualizing subvarieties of mod Λ closed under F -extensions have F -almost split sequences. Let T be an F -cotilting module in mod Λ and S a cotilting module over Γ = End(T ). Then Hom(−, T ) induces a duality between F -almost split sequences in ⊥F T and almost sp...

A new C*-enlargement of a C*-algebra A nested between the local multiplier algebra Mloc(A) of A and its injective envelope I(A) is introduced. Various aspects of this maximal C*-algebra of quotients, Qmax(A), are studied, notably in the setting of AW*algebras. As a by-product we obtain a new example of a type I C*-algebra A such that Mloc(Mloc(A)) 6= Mloc(A).

‎A topological space is called submaximal if each of its dense subsets is open and is called nodec if each of its nowhere dense ea subsets is closed‎. ‎Here‎, ‎we study a variety of spaces some of which have already been studied in $C(X)$‎. ‎Among them are‎, ‎most importantly‎, ‎quasi $P$-spaces and pointwise quasi $P$-spaces‎. ‎We obtain some new useful topological characterizations of quasi $...

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...

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 ...

We present a completed list of polynomial dominanting maps of C2 with branched value curve isomorphic to the complex line C, up to polynomial automorphisms. AMS Classification : 14 E20, 14 B25. 1. Let f : C −→ C be a polynomial dominanting map, Close(f(C)) = C, and denote by degf the geometric degree of f the number of solutions of the equation f = a for generic points a ∈ C. The branched value...

In this paper, we introduce the concept of linear v{C}ech closure spaces and establish the properties of open sets in linear v{C}ech closure spaces (Lv{C}CS). Here, we observe that the concept of linearity is preserved by semi-open sets, g-semi open sets, $gamma$-open sets, sgc-dense sets and compact sets in Lv{C}CS. We also discuss the concept of relative v{C}ech closure operator, meet and pro...

If for any maximal right ideal P of B and a ∈ N(B) ,aB/ aP is almost N-injective, then ring said to be generalized N-injective. In this article, we present some significant findings that are known N-injective rings demonstrate they hold rings. At the same time, study case in which every S.S.Right B-module