A Result on Assosymmetric Rings Satisfying the Ascending Chain Condition

Karamsi, Jayalakshmi; Nageswari, G.

doi:10.20454/ijas.2012.390

Int. J. of Algeb. and Stat.

2012

DOI: 10.20454/ijas.2012.390

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A Result on Assosymmetric Rings Satisfying the Ascending Chain Condition

Jayalakshmi Karamsi¹,

G. Nageswari²

Abstract: Abstract.In this paper we show that if R is a semiprime assosymmetric ring with ascending chain condition for the right annihilators of the form r(x), x∈N(R), and also R contains no infinite direct sums of nonzero right ideals then the right quotient ring of R relative to S exists and it is semisimple and artinian.

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2014

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Left quotient rings of assosymmetric rings

Jayalakshmi

Nageswari

2014

Int. J. of Algeb. and Stat.

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In this paper, we prove the Common-Denominator property. If $Q$ is Weak Fountain-Golden Left order in an assosymmetric ring $R$, then given $b_{1}$,..., $b_{n} \in R$ there exist $a\in S$, $q_{1}$,..., $q_{n}\in Q$ such that for every $i = 1,...,n$, $b_{i} = \tilde{a} q_{i}0$ and $a \tilde{a} q_{i}=q_{i}$ and also it is shown that if $Q$ is subring of an assosymmetric ring $R$, (i) if $R$ is a weak Fountain-Gould left quotient ring of $Q$, then $R$ is a left quotient ring of $Q$, (ii) suppose $R$ nondegenerate and coinciding with its socle, if $Q$ is a weak Fountain-Gould left order in $R$ then $Q$ is a Fountain-Gould left order in $R$, (iii) if $R$ is also artinian then $Q$ is a classical left order in $R$ if and only if $Q$ is a Fountain-Gould left order in $R$.

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Left quotient rings of assosymmetric rings

Jayalakshmi

Nageswari

2014

Int. J. of Algeb. and Stat.

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show abstract

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A Result on Assosymmetric Rings Satisfying the Ascending Chain Condition

Cited by 1 publication

References 5 publications

Left quotient rings of assosymmetric rings

Left quotient rings of assosymmetric rings

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