In the theory of modules over commutative rings there are several possibilities of defining associated prime ideals. The usual definition of an associated prime ideal p for a module M is that p is the annihilator of an element of M . In [2] §1 exercise 17 a generalization of this notion is given. p is called weakly associated (faiblement associé) to M if p is minimal in the set of the prime ide...

Let K be an arbitrary field of characteristic not equal to 2. Let m,n ∈ N and V be an m dimensional orthogonal space over K. There is a right action of the Brauer algebra Bn(m) on the n-tensor space V ⊗n which centralizes the left action of the orthogonal group O(V ). Recently G.I. Lehrer and R.B. Zhang defined certain quasiidempotents Ei in Bn(m) (see (1.1)) and proved that the annihilator of ...

Introduction. In this paper we give a sufficient condition that an algebra have a minimal left (or right) ideal. Specifically, we prove that if A is a complex semisimple Banach algebra with the property that the spectrum of every element in A is at most countable, then A has a minimal left ideal. If A is an ^4*-algebra, we prove that A has a minimal left ideal if the spectrum of every self-adjo...

Let $R$ be a commutative ring with identity, and $ mathrm{A}(R) $ be the set of ideals with non-zero annihilator. The annihilating-ideal graph of $ R $ is defined as the graph $AG(R)$ with the vertex set $ mathrm{A}(R)^{*}=mathrm{A}(R)setminuslbrace 0rbrace $ and two distinct vertices $ I $ and $ J $ are adjacent if and only if $ IJ=0 $. In this paper, conditions under which $AG(R)$ is either E...

Let $R$ be a ring, $sigma$ be an endomorphism of $R$ and $M_R$ be a $sigma$-rigid module. A module $M_R$ is called quasi-Baer if the right annihilator of a principal submodule of $R$ is generated by an idempotent. It is shown that an $R$-module $M_R$ is a quasi-Baer module if and only if $M[[x]]$ is a quasi-Baer module over the skew power series ring $R[[x,sigma]]$.

In this paper, we obtain a classification of quasigroup rings by the quantity elements with null left annihilator for different quasigroups. This becomes possible due to criterion being an element in ring. By virtue criterion, make calculation find regularities using various fields and quasigroups order 4. outcome helps us two results where any have same number ring GF(p)Q fixed Q has GF(pn)Q.