<abstract xml:lang="eb" xmlns="http://www.w3.org/1999/xhtml"><p> In this paper, we consider graded near-rings over a monoid G as generalizations of graded rings over groups, and study some of their basic properties. We give some examples of graded near-rings having various interesting properties, and we define and study the Gop-graded ring associated to a G-graded abelian near-ring, where G is a left cancellative monoid and Gop is its opposite monoid. We also compute the graded ring associated to the graded near-ring of polynomials (over a commutative ring R) whose constant term is zero. </p></abstract>

In this paper, we consider graded near-rings over a monoid G as generalizations of graded rings over groups, and study some of their basic properties. We give some examples of graded near-rings having various interesting properties, and we define and study the Gop-graded ring associated to a G-graded abelian near-ring, where G is a left cancellative monoid and Gop is its opposite monoid. We also compute the graded ring associated to the graded near-ring of polynomials (over a commutative ring R) whose constant term is zero.

Graded near-rings

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"Graded near-rings"}

In this paper, we consider graded near-rings over a monoid G as generalizations of graded rings over groups, and study some of their basic properties. We give...

Graded near-rings

Published Online: Sep 21, 2017

Page range: 201 - 216

Received: Aug 12, 2014

Accepted: Sep 10, 2014

DOI: https://doi.org/10.1515/auom-2016-0011

Keywords
near-ring, graded near-ring, graded ring associated to a graded abelian near-ring

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Graded near-rings

Published Online: Sep 21, 2017

Page range: 201 - 216

Received: Aug 12, 2014

Accepted: Sep 10, 2014

DOI: https://doi.org/10.1515/auom-2016-0011

Keywordsnear-ring, graded near-ring, graded ring associated to a graded abelian near-ring

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
near-ring, graded near-ring, graded ring associated to a graded abelian near-ring