• Dr.G.Sugantha
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In this paper we introduce a new type of near-ring. In [1] R.Balakrishnan and S.Silviya defined a right near-ring N to be a B1 near-ring if for every a ∈ N, there exists x ∈N∗ such that Nax = Nxa. Motivated by this, we introduce the concept of β1 near-rings by defining that N is β1if xNy= Nxy for all x, y in N. We discuss the properties of this newly introduced structure. We prove that in a β1 near-ring with mate functions, the set of all N-subgroups is a Boolean algebra under the usual set inclusion.

near-ring, ideal, Boolean algebra.

"A Special Near -Ring Structure", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.6, Issue 1, page no.513-519, January-2019, Available :http://www.jetir.org/papers/JETIR1901567.pdf

"A Special Near -Ring Structure", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.6, Issue 1, page no. pp513-519, January-2019, Available at : http://www.jetir.org/papers/JETIR1901567.pdf