A Complete Ideals Derivation in Bcik – Algebras

In this paper, introduced a new notions of N sub algebras. closed, commutative, retrenched N ideals, negative functions, and translations are introduced, and related properties are investigated. Characterizations of an N sub algebra and a Commutative N ideal are given. Relations between an N sub algebra an N ideal and commutative N ideal are discussed. We verify that every translations of an N sub algebra resp. N ideal is a retrenched N sub algebra resp.retrenched N ideals . Already introduced a notationof prime ideal in BCIK – algebra show that it is equivalent to the last definition of prime ideal in lower BCIK – Semi lattices. Then we attempt to generalized some useful theorems about prime ideals, in BCIK algebras, instead of lower BCIK Semi lattices. We already investigate some results for PI lattices being a new classical of BCIK–lattices. Specially, we prove that any Boolean lattice is a PI lattice and we show that if X is a PI lattice with bounded commutative, then X is an involutory BCIK algebra if and only if X is a commutative BCIK algebra. Dr. S Rethina Kumar "A Complete Ideals Derivation in Bcik – Algebras" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-5 | Issue-4 , June 2021, URL: https://www.ijtsrd.compapers/ijtsrd40040.pdf Paper URL: https://www.ijtsrd.commathemetics/algebra/40040/a-complete-ideals-derivation-in-bcik-–-algebras/dr-s-rethina-kumar