We develop the theory of Hopf bimodules for a finite rigid tensor category C. Then we use this theory to define a distinguished invertible object D of C and an isomorphism of tensor functors δ : V ∗∗ → D⊗∗∗V ⊗D. This provides a categorical generalization of Radford’s S formula for finite dimensional Hopf algebras [R1], which was proved in [N] for weak Hopf algebras, in [HN] for quasi-Hopf algeb...

‎Let $M$ be a non-zero finitely generated module over a commutative Noetherian local ring $(R,mathfrak{m})$ with $dim_R(M)=t$‎. ‎Let $I$ be an ideal of $R$ with $grade(I,M)=c$‎. ‎In this article we will investigate several natural homomorphisms of local cohomology modules‎. ‎The main purpose of this article is to investigate when the natural homomorphisms $gamma‎: ‎Tor^{R}_c(k,H^c_I(M))to kotim...

We show that there are no automorphic Banach spaces of the form C(K) with K continuous image of Valdivia compact except the spaces c0(Γ). Nevertheless, when K is an Eberlein compact of finite height such that C(K) is not isomorphic to c0(Γ), all isomorphism between subspaces of C(K) of size less than אω extend to automorphisms of C(K).

We classify all essential extensions of the form 0 → B → D → C(X) → 0 where B is a nonunital simple separable finite real rank zero Z-stable C*algebra with continuous scale, and where X is a finite CW complex. In fact, we prove that there is a group isomorphism Ext(C(X),B) → KK(C(X),M(B)/B).

the concepts of fuzzy semi-ideals of r with respect to h≤r and generalized fuzzy quotient rings are introduced. some properties of fuzzy semiideals are discussed. finally, several isomorphism theorems for generalized fuzzy quotient rings are established.

in this paper, we introduce some properties of an intuitionistic normal fuzzy m-subgroup of m- group with m-homomorphism and isomorphism. we study he image, the pre-image and the inverse mapping of the intuitionistic normal fuzzy m-‎subgroups.‎