The nilpotent endomorphisms over a finite free module over a domain with principal ideal are characterized. One may apply these results to the study of the maximal Cohen-Macaulay modules over the ring R := A[[x]]/(x), n ≥ 2, where A is a DVR. Subject Classification: 15A21, 13C14.

Using symmetric algebras we simplify (and slightly strengthen) the Bruns-Eisenbud-Evans “generalized principal ideal theorem” on the height of order ideals of nonminimal generators in a module. We also obtain a simple proof and an extension of a result by Kwieciński, which estimates the height of certain Fitting ideals of modules having an equidimensional symmetric algebra.

L et I be an ideal, homogeneous with respect to the usual grading, in a polynomial ring R = k[x0, . . . , xn] in n+ 1 variables (over an algebraically closed field k). Denote the graded component of I of degree d by Id, and likewise the k-vector space of homogeneous forms of R of degree d by Rd. Since I is a graded R-module, we have k-linear maps μd,i : Id ⊗ Ri → Id+i given for each i and d by ...

Let $R$ be a commutative Noetherian ring with non-zero identity and $fa$ an ideal of $R$. Let $M$ be a finite $R$--module of finite projective dimension and $N$ an arbitrary finite $R$--module. We characterize the membership of the generalized local cohomology modules $lc^{i}_{fa}(M,N)$ in certain Serre subcategories of the category of modules from upper bounds. We define and study the properti...

The free abelian group R(Q) on the set of indecomposable representations of a quiver Q, over a field K, has a ring structure where the multiplication is given by the tensor product. We show that if Q is a rooted tree (an oriented tree with a unique sink), then the ring R(Q)red is a finitely generated Z-module (here R(Q)red is the ring R(Q) modulo the ideal of all nilpotent elements). We will de...

et  be a commutative Noetherian ring,  and  two ideals of  and  a finite -module. In this paper, we have studied the vanishing and relative Cohen-Macaulyness of the functor for relative Cohen-Macauly filtered modules with respect to the ideal  (RCMF). We have shown that the for relative Cohen-Macaulay modules holds for any relative Cohen-Macauly module with respect to  with ........

All rings are commutative with identity and all modules are unitary. In this note we give some properties of a finite collection of submodules such that the sum of any two distinct members is multiplication, generalizing those which characterize arithmetical rings. Using these properties we are able to give a concise proof of Patrick Smith’s theorem stating conditions ensuring that the sum and ...

We determine the ideal structure of the Toeplitz C∗-algebra on the bidisk 0 Introduction A large part of doing research in mathematics is asking the right question. Posing a timely question can trigger thought and provoke insights, even when the matter has no good resolution. That is what happened in the case at hand. After devoting much time to the study of Hilbert modules and quotient Hilbert...

This work is devoted for the design and FPGA implementation of a 16bit Arithmetic module, which uses Vedic Mathematics algorithms. For arithmetic multiplication various Vedic multiplication techniques like Urdhva Tiryakbhyam Nikhilam and Anurupye has been thoroughly analyzed. Also Karatsuba algorithm for multiplication has been discussed. It has been found that Urdhva Tiryakbhyam Sutra is most ...