Study of Some Problems Associated with Semirings and Gamma Semirings - Softcover

Saha, Bibhas Chandra

Softcover

ISBN 10: 3639242823 ISBN 13: 9783639242829

Publisher: VDM Verlag Dr. Müller, 2011

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.

About this title

About the Author

M. Sc.: Burdwan University, India, Ph. D.: Jadavpur University, India, Subject of Interset: Algebra, Analysis, Topology, Publication: 9 research papers in various journals, Present Posotion: Assistant Professor in Department of Mathematics, Chandidas Mahavidyalaya, Khujutipara, India.

Edition details

• Publisher: VDM Verlag Dr. Müller
• Publication date: 2011
• Language: English
• ISBN 10: 3639242823
• ISBN 13: 9783639242829
• Binding: Paperback
• Number of pages: 168