Some Studies on Semirings

  IJMTT-book-cover
 
International Journal of Mathematical Trends and Technology (IJMTT)          
 
© 2013 by IJMTT Journal
Volume-4 Issue-11                           
Year of Publication : 2013
Authors : Y.Monikarchana , N.Sulochana

MLA

Y.Monikarchana , N.Sulochana"Some Studies on Semirings"International Journal of Mathematical Trends and Technology (IJMTT),V4(11):344-349 2013. Published by Seventh Sense Research Group.

Abstract
In this paper, we study the structures of Boolean Semirings and multiplicatively semirings. We proved that, Let S be a multiplicatively subidempotent semiring which contains multiplicative identity 1 which is also additive identity. Then (i) S is viterbi semiring. (ii) (S, +) is commutative. We framed an example for this theorem by considering three element set.

References

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[2] Jonathan S. Golan, “Semrings and their Applications”, Kluwer Academic Publishers, Dordrecht, 1999.
[3] Swaminathan V: On Foster’s Boolean- like rings, Math. Seminar Notes, Kobe University, Japan, Vol 8, 1980, 347-367
[4] T. Vasanthi and N. Sulochana, On the Additive and Multiplicative Structure of Semirings, Annals of Pure and Applied Mathematics - Vol. 3, No. 1, 2013, 78-84.
[5] T.Vasanthi and M.Amala, Structure of Certain Classes of Semirings, International Journal of Mathematical Archive, 4 (9) (2013), 92 - 96.
[6] Vasanthi. T, Monikarchana. Y, Manjula.K, “Structure of Semirings”, Southeast Asian Bulletin of Mathematics. Vol.35, (2011), PP.149- 156.
[7] T.Vasanthi, “Semirings with IMP”, Southeast Asian Bulletin of Mathematics, 32(3) (2008),pp. 995 – 998.

Keywords
Absorbing, Positive Rational Domain (PRD), Viterbi semiring, Weak commutative, Zeroid.