JP Journal of Algebra, Number Theory and Applications
Volume 42, Issue 2, Pages 239 - 253
(May 2019) http://dx.doi.org/10.17654/NT042020239 |
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ON k-IDEALS AND FULL k-IDEALS OF NEAR LEFT ALMOST RINGS
Jay Lord P. Omayao
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Abstract: A near left almost ring (nLA-ring) is a nonempty set N with two binary operations, “+” and “•”, such that (i) (N, +) is an LA-group with 0 as its identity, (ii) (N, •) is an LA-semigroup and (iii) the left distributive property of “•” over “+” holds, that is, for all a, b, c in N. A nonempty subset S of an nLA-ring N is said to be an nLA-subring if S is itself an nLA-ring under the same binary operations as in N. An nLA-subring I of an nLA-ring N is a left ideal, if and is called a right ideal if for all and such that and a two sided ideal if it is both a left and a right ideal. In this paper, we extend the idea of k‑ideals and full k-ideals of semiring to near left almost ring (nLA‑ring). We define an additive inversive near left almost ring and prove some properties similar to semirings. Moreover, we concentrate on restriction in k-ideals and establish some results of full k-ideals and k-closure in an additive inversive near left almost ring. |
Keywords and phrases: nLA-rings, k-ideals, full k-ideals, k-closure.
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