MORE CONDITIONS ON A $ \Gamma- $ SEMIRING AND IDEALS OF A IZUKA AND BOURNE FACTOR $\Gamma-$ SEMIRING

Print ISSN: 0972-7752 | Online ISSN: 2582-0850 | Total Downloads : 27

Abstract

In this paper, we impose some more conditions on a $\Gamma-$ semiring such as cancellative, centreless, semi subtractive, zero divisor, simple and characterize the results of a semiring by using cancellative semi- subtractive, zero divisor of cancellative semi- subtractive and cancellative rigid semi- subtractive $\Gamma-$ semiring with a strong identity. Furthermore, we study maximal and minimal ideals of strongly multiplicative $\Gamma-$ idempotent $\Gamma-$ semiring and the results regarding division $\Gamma-$ semiring, $\Gamma-$ semi field and $\Gamma-$ field for Izuka and Borne factor $\Gamma-$ semiring.

Keywords and Phrases

Multiplicatively cancellative $\Gamma-$ semiring, semi - subtractive, maximal and minimal ideals, division $\Gamma-$ semiring, Bourne and Izuka $\Gamma-$ congruence relation.

A.M.S. subject classification

16Y60, 12E15, 46J20, 06B10, 12K10.

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