IJPAM: Volume 69, No. 4 (2011)

THE INTERSECTION PROPERTY OF QUASI-IDEALS IN
RINGS OF STRICTLY UPPER TRIANGULAR
MATRICES OVER $\mathbb{Z}_m$

Samruam Baupradist$^1$, Ronnason Chinram$^{2,3}$
$^1$Department of Mathematics
Faculty of Science
Chulalongkorn University
Bangkok, 10330, THAILAND
e-mail: samruam.b@chula.ac.th
$^2$Department of Mathematics and Statistics
Faculty of Science
Prince of Songkla University
Hat Yai, Songkhla, 90110, THAILAND
e-mail: ronnason.c@psu.ac.th
$^3$Centre of Excellence in Mathematics
CHE, Si Ayuthaya Road
Bangkok, 10400, THAILAND


Abstract. The notion of quasi-ideals for rings was first introduced by O. Steinfeld. It is known that the intersection of a left ideal and a right ideal of a ring $R$ is a quasi-ideal of $R$. However, a quasi-ideal of $R$ need not be obtained in this way. A quasi-ideal $Q$ of $R$ is said to have the intersection property if $Q$ is the intersection of a left ideal and a right ideal of $R$. If every quasi-ideal of $R$ has the intersection property, $R$ is said to have the intersection property of quasi-ideals. Let $SU_n(R)$ denote the ring of all strictly upper triangular $n\times n$ matrices over a ring $R$. In this paper, we characterize when the ring $SU_n(\mathbb{Z}_m)$ has the intersection property of quasi-ideals.

Received: March 18, 2011

AMS Subject Classification: 16S50

Key Words and Phrases: quasi-ideals, rings of integers modulo $m$, rings of strictly upper triangular matrices, the intersection property of quasi-ideals

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2011
Volume: 69
Issue: 4