In this paper, we continue our study on HvMV-algebras. The quotient structure of an HvMV-algebra by a suitable types of congruences is studied and some properties and related results are given. Some homomorphism theorems are given, as well. Also, the fundamental HvMV-algebra and the direct product of a family of HvMV-algebras are investigated and some related results are obtained.

In this paper we show that if A is a unital Banach algebra and B is a purely innite C*-algebra such that has a non-zero commutative maximal ideal and $phi:A rightarrow B$ is a unital surjective spectrum preserving linear map. Then $phi$ is a Jordan homomorphism.

Let $A$ be a $C^*$-algebra and $E$ be a left Hilbert $A$-module. In this paper we define a product on $E$ that making it into a Banach algebra and show that under the certain conditions $E$  is Arens regular. We also study the relationship between derivations of $A$ and $E$.

Let denote a bipartite distance-regular graph with diameter D ≥ 4, valency k ≥ 3, and distinct eigenvalues θ0 > θ1 > · · · > θD . Let M denote the Bose-Mesner algebra of . For 0 ≤ i ≤ D, let Ei denote the primitive idempotent of M associated with θi . We refer to E0 and ED as the trivial idempotents of M . Let E, F denote primitive idempotents of M . We say the pair E, F is taut whenever (i) E,...

A Banach lattice algebra is a Banach lattice, an associative algebra with a sub-multiplicative norm and the product of positive elements should be positive. In this note we study the Arens regularity and cohomological properties of Banach lattice algebras.

The articles in this Frontiers Research Topic describe how neurons integrate the signals carried by cyclic nucleotide. Three articles present original research, two papers provide provocative opinions about aspects of cyclic nucleotides signaling and four reviews provide timely summary and analysis of the state of the field. The three original articles illustrate how biosensors can reveal the d...

Microscopic lumbar spinous process–splitting laminectomy (LSPSL) has been previously reported as the least invasive surgery for patients with lumbar spinal canal stenosis (LSS). An 18-mm diameter tubular retractor was inserted between the split spinous processes and complete microscopic laminectomy performed in single-level decompressions. A cervical retractor was used to open the caudal parts ...

we study algebraic properties of categories of merotopic, nearness, and filter algebras. we show that the category of filter torsion free abelian groups is an epireflective subcategory of the category of filter abelian groups. the forgetful functor from the category of filter rings to filter monoids is essentially algebraic and the forgetful functor from the category of filter groups to the cat...