let $r$ be a commutative ring with identity and $m$ be a unitary$r$-module. the primary-like spectrum $spec_l(m)$ is thecollection of all primary-like submodules $q$ such that $m/q$ is aprimeful $r$-module. here, $m$ is defined to be rsp if $rad(q)$ isa prime submodule for all $qin spec_l(m)$. this class containsthe family of multiplication modules properly. the purpose of thispaper is to intro...

Often A is called H-module algebra. We refer reader to [11, 6] for the basic information concerning Hopf algebras and their actions on associative algebras. Definition 1.2 The invariants of H in A is the set AH of those a ∈ A, that ha = ε(h)a for each h ∈ H. Straightforward computations show, that AH is subalgebra of A. The notion of action of Hopf algebra on associative algebra generalize the ...

Let S = k[x1, . . . , xn] be a polynomial ring over a field k with n variables x1, . . . , xn, m the irrelevant maximal ideal of S, I a monomial ideal in S and I ′ the polarization of I in the polynomial ring S′ with ρ variables. We show that each graded piece H i m (S/I)a, a ∈ Z , of the local cohomology module H i m (S/I) is isomorphic to a specific graded pieceH i+ρ−n m ′ (S′/I )α, α ∈ Z , o...

EÎ'(X, A) = Ê\T, H\X, A)) where H denotes the Tate cohomology ofir [l, Chapter 12 ] and H'(X, A) is the jth Cech cohomology group of (X, A) with arbitrary coefficients and with w action induced by that on X. The term Ew is the graded module associated with a certain filtered module J*(XyA). This sequence is natural with respect to ir-equivariant maps of (X, A). If w acts trivially on X, the seq...

In the present paper, the concepts of module (uniform) approximate amenability and contractibility of Banach algebras that are modules over another Banach algebra, are introduced. The general theory is developed and some hereditary properties are given. In analogy with the Banach algebraic approximate amenability, it is shown that module approximate amenability and contractibility are the same ...

We consider the problem of calculating the Hurewicz image of Mahowald’s family ηi ∈ 2π S 2 . This allows us to identify specific spherical classes in H∗Ω 2−8+k 0 S 2−2 for 0 6 k 6 6. We then identify the type of the subalgebras that these classes give rise to, and calculate the A-module and R-module structure of these subalgebras. We shall the discuss the relation of these calculations to the C...

Let A be a finite dimensional Hopf algebra, D(A) = A ⊗A its Drinfel’d double and H(A) = A#A its Heisenberg double. The relation between D(A) and H(A) has been found by J.-H. Lu in [24] (see also [33], p. 196): the multiplication of H(A) may be obtained by twisting the multiplication of D(A) by a certain left 2-cocycle which in turn is obtained from the R-matrix of D(A). It was also obtained in ...

‎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 define super Hilbert module and investigate frames in this space. Super Hilbert modules are  generalization of super Hilbert spaces in Hilbert C*-module setting. Also, we define frames in a super Hilbert module and characterize them by using of the concept of g-frames in a Hilbert C*-module. Finally, disjoint frames in Hilbert C*-modules are introduced and investigated.

Let R = ⊕ n∈N0 Rn be a Noetherian homogeneous ring with local base ring (R0,m0) and irrelevant ideal R+, let M be a finitely generated graded R− module. In this paper we show that if R0 is a local ring of dimension one, then H i R+(H 1 m0R (M)) is Artinian for each i ∈ N0. Let f be the least integer such that H i m0R(M) is not finitely generated graded R−module. In this case, we prove that ΓR+(...