let $f: arightarrow b$ be a ring homomorphism and let $j$ be an ideal of $b$. in this paper, we investigate the transfer of the property of coherence to the amalgamation $abowtie^{f}j$. we provide necessary and sufficient conditions for $abowtie^{f}j$ to be a coherent ring.

Let $f: Arightarrow B$ be a ring homomorphism and let $J$ be an ideal of $B$. In this paper, we investigate the transfer of the property of coherence to the amalgamation $Abowtie^{f}J$. We provide necessary and sufficient conditions for $Abowtie^{f}J$ to be a coherent ring.

Let $f : A rightarrow B$ be a ring homomorphism and $J$ an ideal of $B$. In this paper, we give a necessary and sufficient condition for the amalgamated algebra along an ideal $Abowtie^fJ$ to be $J$-Noetherian. Then we give a characterization for pseudo-irreducible ideals of $Abowtie^fJ$, in special cases.

Let $R$ and $S$ be commutative rings with unity, $f\colon R\rightarrow S$ a ring homomorphism $J$ an ideal of $S$. Then the subring $R\bowtie ^fJ:=\lbrace (a,f(a)+j)\mid a\in R$ $j\in J\rbrace $ $R\times is called amalgamation along respect to $f$. In this paper, we determine when ^fJ$ (generalized) filter ring.

We calculate the microstates free entropy dimension of natural generators in an amalgamated free product of certain von Neumann algebras, with amalgamation over a hyperfinite subalgebra. In particular, some ‘exotic’ Popa algebra generators of free group factors are shown to have the expected free entropy dimension. We also show that microstates and non–microstates free entropy dimension agree f...

Let $R$ be a commutative ring with $1 \ne 0$ and let $m$ and
 $n$ integers $1\leq n < m$. A proper ideal $I$ of is
 called an $(m, n)$-closed if whenever $a^m \in I$ for
 some $a\in R$ implies $a^n I$. $ f:A\rightarrow B$ a
 homomorphism $J$ $B.$ This paper
 investigates the concept $(m,n)$-closed ideals in the
 amalgamation $A$ $B$ along respect $f$ denoted by&...

In the spirit of Diffie Hellman the concept of a protocol algebra is introduced using certain amalgamated free product of Braid group (B) and Thompson group (T ) together with a nilpotent subgroup H of index 2

38 and the rich amount of interesting relationships between them, are now well-understood (e.g., Co83, Ma88]). We believe that free amalgamation, rational amalgamation and a further construction called \innnite amalgamation" (still to be investigated) reeect this role on the higher level of amalgamation constructions. Many of the results that we have obtained for free and rational amalgamation ...