of ZfiΓ-modules and ZH-homomorphisms will be called an augmentation sequence if A is a finitely generated Ziϊ-module. Since ZH is a noetherian ring, A is then a finitely presented Zff-module; also, the module B in an augmentation sequence is finitely presented, since it is isomorphic to a submodule of A. For instance, if L £ S is a tame link of m components, G = π^S — L), and G is the commutato...

‎We say that a module $M$ is a emph{cms-module} if‎, ‎for every cofinite submodule $N$ of $M$‎, ‎there exist submodules $K$ and $K^{'}$ of $M$ such that $K$ is a supplement of $N$‎, ‎and $K$‎, ‎$K^{'}$ are mutual supplements in $M$‎. ‎In this article‎, ‎the various properties of cms-modules are given as a generalization of $oplus$-cofinitely supplemented modules‎. ‎In particular‎, ‎we prove tha...

In this paper, we nd the relationships between module contractibility of aBanach algebra and its ideals. We also prove that module contractibility ofa Banach algebra is equivalent to module contractibility of its module uniti-zation. Finally, we show that when a maximal group homomorphic image ofan inverse semigroup S with the set of idempotents E is nite, the moduleprojective tensor product l1...

 The class of ads modules with the SIP (briefly‎, ‎$SA$-modules) is studied‎. ‎Various conditions for a module to be $SA$-module are given‎. ‎It is proved that for a quasi-continuous module $M$‎, ‎$M$ is a UC-module if and only if $M$ is an $SA$-module‎. ‎Also‎, ‎it is proved that the direct sum of two $SA$-modules as $R$-modules is an $SA$-module when $R$ is the sum of the annihilators of thes...

a module $m$ is said to be coretractable if there exists a nonzero homomorphism of every nonzero factor of $m$ into $m$. we prove that all right (left) modules over a ring are coretractable if and only if the ring is morita equivalent to a finite product of local right and left perfect rings.

We present an Avoidance Principle for certain graded rings. As an application we fill a gap in the proof of a result by Brodmann, Rohrer and Sazeedeh about the antipolynomiality of the Hilbert-Samuel multiplicity of the graded components of the local cohomology modules of a finitely generated module over a Noetherian homogeneous ring with two-dimensional local base ring. Let R = ⊕ n∈N0 Rn be a ...

In this paper, we first introduce the concept of single elements in a module. A systematic study of single elements in the AlgL-module U is initiated, where L is a completely distributive subspace lattice on a Hilbert space H. Furthermore, as an application of single elements, we study module isomorphisms between norm closed AlgN -modules, where N is a nest, and obtain the following result: Sup...

The two most fundamental conjectures on the structure of generic Hecke algebra $\mathcal{H}(W)$ associated with a complex reflection group $W$ state that is free module rank $|W|$ over its ring definition, and admits canonical symmetrising trace. first conjecture has recently become theorem, while second conjecture, known to hold for real groups, only been proved some exceptional non-real group...

Let H be a Hopf algebra with bijective antipode, α, β ∈ AutHopf (H) and M a finite dimensional (α, β)-Yetter-Drinfeld module. We prove that End(M) endowed with certain structures becomes an H-Azumaya algebra, and the set of H-Azumaya algebras of this type is a subgroup of BQ(k,H), the Brauer group of H .

Let Λ be a ring endowed with an involution a 7→ ã. We say that two units a and b of Λ fixed under the involution are congruent if there exists an element u ∈ Λ× such that a = ubũ. We denote by H(Λ) the set of congruence classes. In this paper we consider the case where Λ is an order with involution in a semisimple algebraA over a local field and study the question whether the natural map H(Λ)→ ...