in this paper, we study some ring theoretic properties of the amalgamated duplication ring $rbowtie i$ of a commutative noetherian ring $r$ along an ideal $i$ of $r$ which was introduced by d'anna and fontana. indeed, it is determined that when $rbowtie i$ satisfies serre's conditions $(r_n)$ and $(s_n)$, and when is a normal ring, a generalized cohen-macaulay ring and finally a filter ring.

A ring R is called clean if every element of the sum a unit and an idempotent. Motivated by question proposed Lam on cleanness von Neumann Algebras, Vaš introduced more natural concept for ?-rings, ?-cleanness. More precisely, ?-ring ?- projection (?-invariant idempotent). Let F be finite field G abelian group. In this paper, we introduce two classes involutions group rings form characterize ?-...

In this articlewe study the structure of highestweightmodules for quantumgroups defined over a commutative ring with particular emphasis on the structure theory for invariant bilinear forms on these modules. © 2009 Elsevier B.V. All rights reserved.

In this paper we determine the type, a − invariant, Hilbert f unction and Hilbert series of the base ring of some transversal polymatroid such that its associated cone has dimension n and n + 1 facets.

In these notes we investigate the ring of real polynomials in four variables, which are invariant under the action of the reflection groups [3, 4, 3] and [3, 3, 5]. It is well known that they are rationally generated in degree 2,6,8,12 and 2,12,20,30. We give a different proof of this fact by giving explicit equations for the generating polynomials. 0 Introduction There are four groups generate...