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 $r$ be a commutative ring with identity. an ideal $i$ of a ring $r$is called an annihilating ideal if there exists $rin rsetminus {0}$ such that $ir=(0)$ and an ideal $i$ of$r$ is called an essential ideal if $i$ has non-zero intersectionwith every other non-zero ideal of $r$. thesum-annihilating essential ideal graph of $r$, denoted by $mathcal{ae}_r$, isa graph whose vertex set is the set...

We consider the existence and regularity of weakly polyharmonic almost complex structures on a compact Hermitian manifold $$M^{2m}$$ . Such objects satisfy elliptic system $$[\varDelta ^m J, J]=0$$ weakly. prove general theorem for semilinear systems in critical dimensions (with growth nonlinearities), which includes dimension four six.

Let V be a k-dimensional complex vector space. The Plücker ring of polynomial SL(V ) invariants of a collection of n vectors in V can be alternatively described as the homogeneous coordinate ring of the Grassmannian Gr(k, n). In 2003, using combinatorial tools developed by A. Postnikov, J. Scott showed that the Plücker ring carries a cluster algebra structure. Over the ensuing decade, this has ...

Let G be a group and R G-graded ring. In this paper, we present examine the concept of graded weakly 2-absorbing ideals as in generality prime ring which is not commutative, demonstrates that symmetry obtained lot outcomes commutative rings remain are commutative.

The goal of this paper is to give a definition generalization fuzzy prime $\Gamma $-ideals in $-rings by introducing 2-absorbing and weakly completely commutative their properties. Furthermore, we diagram which transition between definitions $-ring. Finally, introduce quotient $-ring $R$ induced the $-ideal $2$-absorbing

In 2008, Al-Thaga and Shahzad [Generalized I-nonexpansive self-maps and invariant approximations, Acta Math. Sinica 24(5) (2008), 867{876]introduced the notion of occasionally weakly compatible mappings (shortly owcmaps) which is more general than all the commutativity concepts. In the presentpaper, we prove common xed point theorems for families of owc maps in Mengerspaces. As applications to ...

let $r=oplus_{nin bbb n_0}r_n$ be a noetherian homogeneous ring with local base ring $(r_0,frak{m}_0)$, $m$ and $n$ two finitely generated graded $r$-modules. let $t$ be the least integer such that $h^t_{r_+}(m,n)$ is not minimax. we prove that $h^j_{frak{m}_0r}(h^t_{r_+}(m,n))$ is artinian for $j=0,1$. also, we show that if ${rm cd}(r_{+},m,n)=2$ and $tin bbb n_0$, then $h^t_{frak{m}_0r}(h^2_{...

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.