A module MR is called right principally quasi-Baer (or simply right p.q.-Baer) if the right annihilator of a principal submodule of R is generated by an idempotent. Let R be a ring. Let α be an endomorphism of R and MR be a α-compatible module and T = R[[x;α]]. It is shown that M [[x]]T is right p.q.-Baer if and only if MR is right p.q.-Baer and the right annihilator of any countably-generated ...

This paper deals with certain properties of the subspaces of LC(H) and C and namely those connected with the reflexivity and with the property of containing classical spaces. It is proved that any subspace of C (1 < p < oo) is either isomorphic to Hilbert space or it contains a subspace isomorphic to I . For Cj and LC'H) the same results were obtained by J. R. Holub, cf. [4]. Introduction. Let ...

Let $R$ be a commutative ring and let $M$ be an $R$-module. We define the small intersection graph $G(M)$ of $M$ with all non-small proper submodules of $M$ as vertices and two distinct vertices $N, K$ are adjacent if and only if $Ncap K$ is a non-small submodule of $M$. In this article, we investigate the interplay between the graph-theoretic properties of $G(M)$ and algebraic properties of $M...

The notion of intuitinitic (T, S)-fuzzy submodule in Module is introduced, and related properties are investigated. Mathematics Subject Classification: 08A72, 13C99

Let C denote the category of Hilbert modules which are similar to contractive Hilbert modules. It is proved that if H0, H ∈ C and if H1 is similar to an isometric Hilbert module, then the sequence 0 → H0 → H → H1 → 0 splits. Thus the isometric Hilbert modules are projective in C. It follows that ExtC (K, H) = 0, whenever n > 1, for H, K ∈ C. In addition, it is proved that (Hilbert modules simil...

We prove that two dual operator algebras are weak Morita equivalent in the sense of [4] if and only if they have equivalent categories of dual operator modules via completely contractive functors which are also weakcontinuous on appropriate morphism spaces. Moreover, in a fashion similar to the operator algebra case we can characterize such functors as the module normal Haagerup tensor product ...

abstract. certain facts about frames and generalized frames (g- frames) are extended for the g-frames for hilbert c*-modules. it is shown that g-frames for hilbert c*-modules share several useful properties with those for hilbert spaces. the paper also character- izes the operators which preserve the class of g-frames for hilbert c*-modules. moreover, a necessary and suffcient condition is ob- ...

in this paper we proved that every g-riesz basis for hilbert space $h$ with respect to $k$ by adding a condition is a riesz basis for hilbert $b(k)$-module $b(h,k)$. this is an extension of [a. askarizadeh,m. a. dehghan, {em g-frames as special frames}, turk. j. math., 35, (2011) 1-11]. also, we derived similar results for g-orthonormal and orthogonal bases. some relationships between dual fram...

Frames on Hilbert C*-modules have been defined for unital C*algebras by Frank and Larson [5] and operator-valued frames on a Hilbert space have been studied in [8]. The goal of this paper is to introduce operatorvalued frames on a Hilbert C*-module for a σ-unital C*-algebra. Theorem 1.4 reformulates the definition given in [5] in terms of a series of rank-one operators converging in the strict ...

Many Hilbert modules over the polynomial ring in m variables are essentially reductive, that is, have commutators which are compact. Arveson has raised the question of whether the closure of homogeneous ideals inherit this property and provided motivation to seek an affirmative answer. Positive results have been obtained by Arveson, Guo, Wang and the author. More recently, Guo and Wang extended...