Related papers: Amalgamated algebras along an ideal

Let $f:A \rightarrow B$ be a ring homomorphism and let $J$ be an ideal of $B$. In this paper, we study the amalgamation of $A$ with $B$ along $J$ with respect to $f$, a construction that provides a general frame for studying the amalgamated…

Let $f:A \to B$ be a ring homomorphism and let $J$ be an ideal of $B$. In this paper, we study the amalgamation of $A$ with $B$ along $J$ with respect to $f$ (denoted by ${A\Join^fJ}$), a construction that provides a general frame for…

Let $f: A\rightarrow B$ and $g: A\rightarrow C$ be two commutative ring homomorphisms and let $J$ and $J'$ be two ideals of $B$ and $C$, respectively, such that $f^{-1}(J)=g^{-1}(J')$. The \emph{bi-amalgamation} of $A$ with $(B, C)$ along…

Let $f:A\longrightarrow B$ be a ring homomorphism and let $\mathfrak b$ be an ideal of $B$. In this paper we study Pr\"ufer like conditions in the amalgamation of $A$ with $B$ along $\mathfrak b$, with respect to $f$, a ring construction…

Let $f:A\longrightarrow B, g:A\longrightarrow C$ be ring homomorphisms and let $\mathfrak{b}$ (resp., $\mathfrak{c}$) be an ideal of $B$ (resp., $C$) satisfying $f^{-1}(\mathfrak{b})=g^{-1}(\mathfrak{c})$. Recently Kabbaj, Louartiti and…

We introduce a new general construction, denoted by $R\JoinE$, called the amalgamated duplication of a ring $R$ along an $R$--module $E$, that we assume to be an ideal in some overring of $R$. (Note that, when $E^2 =0$, $R\JoinE$ coincides…

Let $f : A \rightarrow B$ be a ring homomorphism and $J$ be an ideal of $B$. In this paper, we investigate the transfer of Gaussian property to the amalgamation of $A$ with $B$ along $J$ with respect to $f$ (denoted by $A\bowtie^fJ),$…

In this work, we investigate the transfer of some homological properties from a ring $R$ to his amalgamated duplication along some ideal $I$ of $R$, and then generate new and original families of rings with these properties.

Let $f: A\rightarrow B$ be a ring homomorphism and $J$ be an ideal of $B$. In this paper, we investigate the transfer of Armendariz-like properties to the amalgamation of $A$ with $B$ along $J$ with respect to $f$ (denoted by $A\bowtie^fJ)$…

Let $f: A\rightarrow B$ be a ring homomorphism and let $J$ be an ideal of $B$. In this paper, we investigate the transfer of self-injective property to the amalgamation of $A$ with $B$ along $J$ with respect to $f$ (denoted by…

The aim of this paper is to study the classical global and weak dimensions of the amalgamated duplication of a ring $R$ along a pure ideal $I$.

Let $A$ and $B$ be commutative rings with unity, $f:A\to B$ a ring homomorphism and $J$ an ideal of $B$. Then the subring $A\bowtie^fJ:=\{(a,f(a)+j)|a\in A$ and $j\in J\}$ of $A\times B$ is called the amalgamation of $A$ with $B$ along $J$…

Let $R$ be a commutative ring and $I$ be an ideal of $R$. The amalgamated duplication of $R$ along $I$ is the subring $R\Join I:=\{(r,r+i)| r\in R, i\in I\}$ of $R\times R$. This paper investigates the extended zero-divisor graph of the…

After recalling briefly the main properties of the amalgamated duplication of a ring $R$ along an ideal $I$, denoted by $R\JoinI$, we restrict our attention to the study of the properties of $R\JoinI$, when $I$ is a multiplicative canonical…

In this paper, we characterize an amalgamated duplication of a ring $R$ along a proper ideal $I$, $R\bowtie I$, which is quasi-Frobenius.

Let $f : A \rightarrow B$ be a ring homomorphism and $J$ be an ideal of $B$. In this paper, we give a characterization of zero divisors of the amalgamation which is a generalization of Maimani's and Yassemi's work (see \cite{y}). Also, we…

Let $f: A\rightarrow B$ be a ring homomorphism and let $J$ be an ideal of $B$. In this paper, we investigate the transfert of the property of coherence to the amalgamation $A\bowtie^{f}J$. We provide necessary and sufficient conditions for…

Let $f:R\to S$ be a ring homomorphism and $J$ be an ideal of $S$. Then the subring $R\bowtie^fJ:=\{(r,f(r)+j)\mid r\in R$ and $j\in J\}$ of $R\times S$ is called the amalgamation of $R$ with $S$ along $J$ with respect to $f$. In this paper,…

Let $A$ and $B$ be commutative rings with unity, $f:A\to B$ a ring homomorphism and $J$ an ideal of $B$. Then the subring $A\bowtie^fJ:=\{(a,f(a)+j)|a\in A$ and $j\in J\}$ of $A\times B$ is called the amalgamation of $A$ with $B$ along with…

Let $R$ and $S$ be commutative rings with identity, $f:R\to S$ a ring homomorphism and $J$ an ideal of $S$. Then the subring $R\bowtie^fJ:=\{(r,f(r)+j)\mid r\in R$ and $j\in J\}$ of $R\times S$ is called the amalgamation of $R$ with $S$…