Geodesic
Regular $\Gamma-$incline and field $\Gamma-$semiring
Novi Sad Journal of Mathematics, Tome 45 (2015) no. 2.

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We introduce the notion of $\Gamma -$incline as a generalization of incline, which is an algebraic structure with an additional poset structure. We introduce the notions of regular $\Gamma -$incline, integral $\Gamma -$incline, field $\Gamma -$incline, field $\Gamma -$semiring, simple $\Gamma -$semiring and pre-integral $\Gamma -$semiring. We study their properties and relations between them. We prove that if $M$ is a linearly ordered regular $\Gamma -$incline, then $M$ is a commutative $\Gamma -$incline and $M$ is a field $\Gamma -$semiring with an additional property if and only if $M$ is an integral, simple and commutative $\Gamma -$semiring.
Publié le :
DOI : 10.30755/NSJOM.2014.058
Classification : 06F25, 16A09
Keywords: $\Gamma -$semiring, $\Gamma -$incline, regular $\Gamma -$incline, integral $\Gamma -$incline, field $\Gamma -$incline, field $\Gamma -$semiring, simple $\Gamma -$semiring 
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     title = {Regular $\Gamma-$incline and field $\Gamma-$semiring},
     journal = {Novi Sad Journal of Mathematics},
     pages = {155 - 171},
     publisher = {mathdoc},
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     year = {2015},
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M. Murali Krishna Rao; B. Venkateswarlu. Regular $\Gamma-$incline and field $\Gamma-$semiring. Novi Sad Journal of Mathematics, Tome 45 (2015) no. 2. doi : 10.30755/NSJOM.2014.058. http://geodesic.mathdoc.fr/articles/10.30755/NSJOM.2014.058/

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