arXiv subjects

Siamak Yassemi

Publications and source records attributed to Siamak Yassemi.

56 records · Page 4Linked to original sources

arXiv2002

Bounds for numbers of generators for a class of submodules of a finitely generated module

The aim of this paper is to obtain a uniform bound for a certain class of submodules from the following theorem: Let $(R,\frak m)$ be a local ring, let $M$ be a finite $R$--module of dimension $d\ge 1$ and let $\frak q$ be an ideal of $R$ generated by a system of parameters on $M$. Let $N$ be a submodule of $M$ with $\depth M/N\ge d-1$. Then $\ell(N/\frak qN)\le\ell(M/\frak qM)$.

math.AC↗

arXiv2002

Cohen--Macaulayness of tensor products

Let $(R,\fm)$ be a commutative Noetherian local ring. Suppose that $M$ and $N$ are finitely generated modules over $R$ such that $M$ has finite projective dimension and such that $\Tor^R_i(M,N)=0$ for all $i>0$. The main result of this note gives a condition on $M$ which is necessary and sufficient for the tensor product of $M$ and $N$ to be a Cohen--Macaulay module over $R$, provided $N$ is itself a Cohen--Macaulay module.

math.AC↗