Properties of Connected Semirings and B-lattice Semirings

 International Journal of Mathematics Trends and Technology (IJMTT) © 2017 by IJMTT Journal Volume-52 Number-6 Year of Publication : 2017 Authors : D.Mrudula Devi, G.ShobhaLatha, T.Padma Praveen 10.14445/22315373/IJMTT-V52P552

D.Mrudula Devi, G.ShobhaLatha, T.Padma Praveen"Properties of Connected Semirings and B-lattice Semirings", International Journal of Mathematics Trends and Technology (IJMTT). V52(6):370-373 December 2017. ISSN:2231-5373. www.ijmttjournal.org. Published by Seventh Sense Research Group.

Abstract
This paper contains some results on connected semirings and b- lattice semirings. We consider a connected semiring (s,+,.,0) satisfying the identity 1+y=y+1 =1 for all y in s in which s is a variant of semi group (or) a-connected semigroup then it is proved that (s,a) is I- Medial, I –Semi Medial, Quasive separative.weakly separative. (S,.) is singular if (S,.) is rectangular band.Again we consider the same identity with (S,.) is commutative if (S,a) is L- Commutative. On the other hand (S,+,.) be a b-lattice semiring then(S,+) is diagonal if (S,+) is singular and the b-lattice semiring satisfying the identity a+b+ab=ab for all a,b in S then (S,+) is semimedial if (S,+) ,(S,.) are singular

Reference
[1] Golan, J.S.“The theory of semi rings with applications in mathematical and theoretical computer science” pitman monographs and survey in pure and applied mathematics, II series (1992)
[2] Hickey, J.B “On variants of semi groups” theory academic press, 1976
[3] Howie, J.M“Introduction to semi group theory” academic press. London, 1976

Keywords
connectedsemiring,I-medial,I-semimedial,rectangularband,quasiveseparative,weakly separative, blattice semi ring..