Let M⊂N$M\subset N$ be Hilbert C∗$C^*$‐modules over a C∗$C^*$‐algebra A$A$ with M⊥=0$M^\perp =0$. It was shown recently by Kaad and Skeide that there exists a non‐zero A$A$‐valued functional on N$N$ ...such that its restriction onto M$M$ is zero. Here, we show that this may happen even if A$A$ is monotone complete. On the other hand, we show that for certain type I W∗$W^*$‐algebras this cannot happen.
Quasi-Coregular Modules Shaibani, Rafid M. AL; Mothafar, Nuhad S. AL
Journal of physics. Conference series,
05/2020, Volume:
1530, Issue:
1
Journal Article
Peer reviewed
Open access
In this paper, we introduce the concept of quasi - copure submodules which is ageneralization of a copure submodules. Weused this concept to define the class of quasi - coregular module, where an ...R-module M iscalled quasi -coregular module if every submodule of M is quasi-co-pure. Many results about thisconcept are proved.
We study non-standard Verma type modules over the Kac-Moody queer Lie superalgebra ð"®(n)(2). We give a sufficient condition under which such modules are irreducible. We also give a classification ...of all irreducible diagonal ℤ-graded modules over certain Heisenberg Lie superalgebras contained in ð"®(n)(2).
In this paper we have introduced the notion of weak reduced module and weak rigid module as the generalizations of reduced module by working on the context of nilpotent elements of module and ...investigated some of its properties. Various results are extended for this generalization and some counter examples are constructed to validate the generalizations.
In this paper, we studied the resolution of Weyl module for characteristic zero in the case of partition (8,7,3) by using mapping Cone which enables us to get the results without depended on the ...resolution of Weyl module for characteristic free for the same partition.
For any module M, the smallest subcategory of R-modules which is a Grothendieck category and contains M is the category σM. In this article, by introducing two classes of R-modules under the titles ...Formula omitted. -modules and Σn-modules, the notions σ-projective and σ-injective dimension in the category σM have been defined and studied. The relationships between these notions and the corresponding notions defined in the category of R-modules have been investigated. Also, σ-global dimension is defined and some of its properties have been studied.
The article describes a method for coordinating the microwave path and verifying the microwave module of the DMVC. The method for coordinating and adjusting the microwave module helps measure and ...evaluate characteristics of the device to confirm compliance with the DMVC requirements.
In this paper we study the superalgebra An, introduced by the authors in previous work on categorification of Verma modules for quantum sl2. The superalgebra An is akin to the nilHecke algebra, and ...shares similar properties. We also prove a uniqueness result about 2-Verma modules on k-linear 2-categories.
On [delta]-semiperfect modules Nguyen, Hau Xuan; Kosan, M Tamer; Zhou, Yiqiang
Communications in algebra,
01/2018, Volume:
46, Issue:
11
Journal Article
Peer reviewed
A submodule N of a module M is δ-small in M if N+Xnot equal toM for any proper submodule X of M with MDIVISION SLASHX singular. A projective δ-cover of a module M is a projective module P with an ...epimorphism to M whose kernel is δ-small in P. A module M is called δ-semiperfect if every factor module of M has a projective δ-cover. In this paper, we prove various properties, including a structure theorem and several characterizations, for δ-semiperfect modules. Our proofs can be adapted to generalize several results of Mares 8 and Nicholson 11 from projective semiperfect modules to arbitrary semiperfect modules.
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