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Book synopsis

In 1964, the notion of Gamma-ring was introduced by N. Nobusawa to provide algebraic home to Hom(A,B) and Hom(B,A) where A, B are additive abelian groups. The notion of semiring was introduced by H. S. Vandiver in 1934. Gamma-semiring was introduced by M.M.K. Rao in 1995 as a generalization of semiring as well as of Gamma-ring. With every Gamma-semiring there corresponds two semirings namely the left operator semiring and the right operator semiring. The natural growth of Gamma-semirings is influenced by two things - one is the generalization of results of Gamma-rings and another is the generalization of results of semirings. Motivated by the efficacy of operator semirings, we introduced here Nobusawa Gamma-semirings. We also explored some relevant aspects of semirings namely h-prime, h-semiprime, F-semiprime ideals of semirings and their subsequent generalization to Gamma-semirings. Finally we define a semiring denoted by S2 = (R, Gamma, S, L) over a Nobusawa Gamma-semiring and combine the study of semiring and Gamma-semiring accomplished so far in the form of obtaining i) characterization of various types of ideals of S2 and ii) connections between S2 and Morita context.

Book details

Book category Books in English Mathematics & science Mathematics Algebra

• Full title: Study of Some Problems Associated with Semirings and Gamma Semirings
• Subtitle: Nobusawa Gamma semirings, ideals, pre-prime and pre-semiprime ideals, h-prime and h-semiprime ideals, F-semiprime ideals, matrix semirings
• Author: Bibhas Chandra Saha
• Language: English
• Binding: Paperback
• Number of pages: 168
• EAN: 9783639242829
• ISBN: 3639242823
• ID: 06831906
• Publisher: VDM Verlag
• Weight: 254 g
• Dimensions: 229 × 152 × 10 mm
• Date of publishing: 11. February 2011

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