let $(r,m)$ be a commutative noetherian local ring, $m$ a finitely generated $r$-module of dimension $d$, and let $i$ be an ideal of definition for $m$. in this paper, we extend cite[corollary 10(4)]{p} and also we show that if $m$ is a cohen-macaulay $r$-module and $d=2$, then $lambda(frac{widetilde{i^nm}}{jwidetilde{i^{n-1}m}})$ does not depend on $j$ for all $ngeq 1$, where $j$ is a minimal ...

ABSTRACT. Let R be a commutative noetherian ring, I and J are two ideals of R. Inthis paper we introduce the concept of (I;J)- minimax R- module, and it is shown thatif M is an (I;J)- minimax R- module and t a non-negative integer such that HiI;J(M) is(I;J)- minimax for all i

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 $(R,m)$ be a commutative Noetherian local ring, $M$ a finitely generated $R$-module of dimension $d$, and let $I$ be an ideal of definition for $M$. In this paper, we extend cite[Corollary 10(4)]{P} and also we show that if $M$ is a Cohen-Macaulay $R$-module and $d=2$, then $lambda(frac{widetilde{I^nM}}{Jwidetilde{I^{n-1}M}})$ does not depend on $J$ for all $ngeq 1$, where $J$ is a minimal ...

Let $R$ be a commutative Noetherian ring and let $fa$, $fb$ be two ideals of $R$ such that $R/({fa+fb})$ is Artinian. Let $M$, $N$ be two finitely generated $R$-modules. We prove that $H_{fb}^j(H_{fa}^t(M,N))$ is Artinian for $j=0,1$, where $t=inf{iin{mathbb{N}_0}: H_{fa}^i(M,N)$ is not finitelygenerated $}$. Also, we prove that if $DimSupp(H_{fa}^i(M,N))leq 2$, then $H_{fb}^1(H_{fa}^i(M,N))$ i...

Let $(R,\mathfrak m)$ be a Noetherian local ring of prime characteristic p > 0, and t an integer such that $H_{\mathfrak m}^{j}(R)/0^{F}_{H^{j}_{\mathfrak m}(R)}$ has finite length for all j < t. The aim this paper is to show there exists uniform bound Frobenius test exponents ideals generated by filter regular sequences at most

We consider algebras over a field K defined by a presentation K〈x1, . . . , xn : R〉, where R consists of ( n 2 ) square-free relations of the form xixj = xkxl with every monomial xixj , i 6= j, appearing in one of the relations. Certain sufficient conditions for the algebra to be noetherian and PI are determined. For this, we prove more generally that right noetherian algebras of finite Gelfand...

The j-multiplicity is an invariant that can be defined for any ideal in a Noetherian local ring (R, m). It is equal to the Hilbert-Samuel multiplicity if the ideal is m-primary. In this paper we explore the computability of the j-multiplicity, giving another proof for the length formula and the additive formula.

We prove that the elements of any standard basis of In, where I is an ideal of a Noetherian local ring and n is a positive integer, have order bounded by a linear function in n. We deduce from this that the elements of any standard basis of In in the sense of Grauert-Hironaka, where I is an ideal of the ring of power series, have order bounded by a polynomial function in n. The aim of this pape...