ACTA CIENCIA INDICA Vol. 27 M No. 1 2001 87-88 TIGHT RINGS AND GROUP RINGS W.B.Vasantha Kandasamy Stojan and C. Miroslav defined the concept of tight semigroups. Motivated by his paper we define the concept of Tight rings. Let R be a ring. R is said to be a tight ring if we can find a subset M of R with |M| ≤ 2, |M + M| ≤ 2 and |M2| ≤ 2, then M is called the tight subset of R. R is a tight ring if and only if M is a subring ( |M2| < 2 ).We define R to a strong tight ring if every subset M of R is a tight subset of R. Clearly a strong right ring is a tight ring. We obtain several nice results in this direction. All Rights Reserved. This work is Copyright © W.B.Vasantha Kandasamy, 2003. Mathematicians can use the above material for research purposes, but the work of the author ∗must∗ be acknowledged. Violators of copyright, and those indulging in plagiarism and intellectual theft are liable for strict prosecution. e-mail: [email protected] web: http://mat.iitm.ac.in/~wbv
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