Articles liés à Study of Some Problems Associated with Semirings and...

Study of Some Problems Associated with Semirings and Gamma Semirings - Couverture souple

Saha, Bibhas Chandra

 
9783639242829: Study of Some Problems Associated with Semirings and Gamma Semirings
Couverture souple
ISBN 10 : 3639242823 ISBN 13 : 9783639242829
Editeur : 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.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

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.

Biographie de l'auteur

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.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
VDM Verlag Dr. Müller
Date d'édition
2011
Langue
anglais
ISBN 10 
3639242823
ISBN 13 
9783639242829
Reliure
Broché
Nombre de pages
168
Coordonnées du fabricant
non disponible
Personne responsable
non disponible