T-fuzzy ideals in ordered Γ-semirings
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초록
In this paper,we introduce the notion of $T-$fuzzy ideal, $T-$fuzzy left (right) $k-$ideal, $T-$fuzzy interior ideal, $T-$fuzzy quasi ideal, $T-$fuzzy bi-ideal in an ordered $\Gamma-$semiring. We characterize the regular ordered $\Gamma-$semiring in terms of $T-$fuzzy left (right) ideal, $T-$fuzzy quasi ideal, $T-$fuzzy bi-ideal, $T-$fuzzy interior ideal and study their properties and relations between them. We establish that $T-$fuzzy ideal, $T-$fuzzy bi-ideal, $T-$fuzzy quasi ideal and $T-$fuzzy interior ideal are equivalent in a regular ordered $\Gamma -$semiring and characterize the simple ordered $\Gamma -$semiring in terms of $T-$fuzzy interior ideal.
Abstract
In this paper,we introduce the notion of $T-$fuzzy ideal, $T-$fuzzy left (right) $k-$ideal, $T-$fuzzy interior ideal, $T-$fuzzy quasi ideal, $T-$fuzzy bi-ideal in an ordered $\Gamma-$semiring. We characterize the regular ordered $\Gamma-$semiring in terms of $T-$fuzzy left (right) ideal, $T-$fuzzy quasi ideal, $T-$fuzzy bi-ideal, $T-$fuzzy interior ideal and study their properties and relations between them. We establish that $T-$fuzzy ideal, $T-$fuzzy bi-ideal, $T-$fuzzy quasi ideal and $T-$fuzzy interior ideal are equivalent in a regular ordered $\Gamma -$semiring and characterize the simple ordered $\Gamma -$semiring in terms of $T-$fuzzy interior ideal.
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