ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

Vol. LXXV, 1 (2006)
p. 137 - 146

Regular additively inverse semirings
M. K. Sen and S. K. Maity

Abstract. In this paper we show that in a regular additively inverse semiring (S, +, ×) with 1 satisfying the conditions
(A) a(a + a') = a + a'; (B) a(b + b') = (b + b')a, and (C) a + a(b + b') = a,
for all a, b Î S, the sum of two principal left ideals is again a principal left ideal. Also, we decompose S as a direct sum of two mutually inverse ideals.

Keywords: Additive inverse semiring, regular semiring, mutually inverse ideals.

AMS Subject classification:16A78, 20M10, 20M07.

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Acta Mathematica Universitatis Comenianae
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