arXiv subjects

Nematollah Shirmohammadi

Publications and source records attributed to Nematollah Shirmohammadi.

5 recordsLinked to original sources

arXiv2026

On monoid graded semihereditary rings

In order to study graded left hereditary and left semihereditary rings graded by a cancelation monoid in terms of their modules, we need to revisit graded free, projective, injective, and flat modules and provide graded versions of specific results concerning these modules, like Baer's criterion on injectivity and Lazard's theorem on flatness. Then, among other things, we can give some characterization of graded left hereditary and left semihereditary rings, in particular, of graded-Prüfer and graded-Dedekind domains.

math.RA↗

arXiv2026

A characterization of monoid graded semihereditary rings

Let $Γ$ be a cancellation monoid and $R=\bigoplus_{α\in Γ}R_α$ be a $Γ$-graded ring. It is shown that $R$ is graded left semihereditary if and only if $R$ is graded left coherent and every graded submodule of a flat left $R$-module is flat. Hence it gives a new characterization of graded-Prüfer domains.

math.RA↗

arXiv2025

On graded going-down domains, II

In this paper we consider the graded going-down property of graded integral domains in pullbacks. It then enables us to give original examples of these domains.

math.AC↗

arXiv2024

On graded Going down domains

Let $Γ$ be a torsionless commutative cancellative monoid and $R =\bigoplus_{α\in Γ}R_α$ be a $Γ$-graded integral domain. In this paper, we introduce the notion of graded going-down domains. Among other things, we provide an equivalent condition for graded-Prüfer domains in terms of graded going-down and graded finite-conductor domains. We also characterize graded going-down domains by means of graded divided domains. As an application, we show that the graded going-down property is stable under factor domains.

math.AC↗

arXiv2016

On Amalgamated Banach algebras

Let $A$ and $B$ be Banach algebras, $θ: A\to B$ be a continuous Banach algebra homomorphism and $I$ be a closed ideal in $B$. Then the direct sum of $A$ and $I$ with respect to $θ$, denoted $A\bowtie^θI$, with a special product becomes a Banach algebra which is called the amalgamated Banach algebra. In this paper, among other things, we compute the topological centre of $A\bowtie^θI$ in terms of that of $A$ and $I$. Using this, we provide a characterization of the Arens regularity of $A\bowtie^θI$. Then we determine the character space of $A\bowtie^θI$ in terms of that of $A$ and $I$. Moreover, we study the weak amenability of $A\bowtie^θI$.

math.FA↗