Properties of Connected Semirings and B-lattice Semirings

D.Mrudula Devi; G.ShobhaLatha; T.Padma Praveen

doi:https://doi.org/10.14445/22315373/IJMTT-V52P552

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 52 | Number 6 | Year 2017 | Article Id. IJMTT-V52P552 | DOI : https://doi.org/10.14445/22315373/IJMTT-V52P552

Properties of Connected Semirings and B-lattice Semirings

D.Mrudula Devi, G.ShobhaLatha, T.Padma Praveen

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.

Keywords

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

References

[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.

Citation :

D.Mrudula Devi, G.ShobhaLatha, T.Padma Praveen, "Properties of Connected Semirings and B-lattice Semirings," International Journal of Mathematics Trends and Technology (IJMTT), vol. 52, no. 6, pp. 370-373, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V52P552