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Identities and left cancellation in distributively generated near-rings

Published online by Cambridge University Press:  09 April 2009

David John
David John
Affiliation:
Department of Mathematics and Computer Science, Valdosta State College, Valdosta, GA 31601, U.S.A.
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Abstract

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Given a semigroup S, we define {N(S), +, ·} to be the ‘free’ distributively generated near-ring. Since all words in N(S) can be expressed as the sum and difference of elements of S, we are able to define a length function on the words of N(S). The following theorems then follow: Theorem 1. N(S) contains a multiplicatice identity e if and only if e ∈ S. Theorem 2. If S is the free semigroup in the cariety of all semi—groups then N(S) is left cancellatice.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 30 , Issue 2 , December 1980 , pp. 238 - 242
Copyright
Copyright © Australian Mathematical Society 1980

References

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