Martindale’s like results in inverse semirings

Sara Shafiq; Muhammad Aslam; Muhammad Yaqoub

doi:10.5269/bspm.v38i6.37439

Sara Shafiq Government College University Mathematics Department
Muhammad Aslam Government College University Mathematics Department
Muhammad Yaqoub Government College University Mathematics Department

DOI: https://doi.org/10.5269/bspm.v38i6.37439

Keywords: Inverse semiring, Prime Semiring, Right S-semimodule, Extended Centroid

Abstract

The purpose of this paper is to study the notion of extended centroid in inverse semirings thereby, we generalize a few well known results of W.S Maritndale to inverse semirings.

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References

S.A Amitsur, On rings of quotients, Sympos. Math., 8 (1972), 149 − 164.

H. E. Bell and W.S Martindale,Centralizing mappings of semiprime rings, Cand. Math. Bull., 30(1987)1, 92 − 101.

M. Bresar, M. A. Chebotar, W. S. Martindale, Functional identities, Birkhauser Verlag, Boston (2007).

M.Bresar, An Introduction to noncommutative Algebra, Universitext, Springer International Publishing Switzerland, 2014.

J.S Golan, The theory of semirings with applications in mathematics and theoretical computer science., John Wiley and Sons. Inc., New York, (1992).

U. Habisch, H.J. Weinert, Semirings- Algebraic theory and applications in computer science, World Scientific, 1993.

B.Hvala, Generalized derivations in Rings,Communication in Algebra, 26(1998)4, 1147−1166.

P.H. Karvellas, Inversive semirings, J. Aust. Math. Soc. 18 (1974), 277 − 288.

V.K Kharchenko, Generalized identities with automorphisms Algebra i Logika, 14 (1975), 215 − 237.

V.K Kharchenko, Galois theory of semiprime rings, Algebra i Logika, 16 (1977), 313 − 363.

C.Lanski, Differential identities, lie ideals and Posner’s theorem, Pacific Journal of Math., 134(1988)2, 275 − 297.

W.S Martindale, Prime rings satisfying a generalized polynomial identity, Journal of Algebra 12(1969), 576 − 584.

S.Montgomery, D.S Passman, Galois theory of prime rings, J. Pure Appl. Algebra, 31 (1984), 139 − 184.

S.Sara, M.Aslam and M.A. Javed On Centralizer of semiprime inverse semirings, Discussiones Mathematicae - General Algebra and Applications, 36 (2016), 71 − 72.

S.Sara, M.Aslam, On Jordan Mappings of inverse semirings, Open Math., 15(2017), 1123 − 1131.

H.Yazarli, M.A. Oztruk, On the centroid of prime semirings,Turk. J. Math. 37 (2013), 577 − 584.