k-Derivations and k-Homomorphisms of Gamma Rings: Jordan k-Derivations, Jordan Left/Right and Generalized k-Derivations, Jordan k-Homomorphisms and anti-k-Homomorphisms - Couverture souple

Chakraborty, Sujoy; Paul, Akhil Chandra

 
9783659178399: k-Derivations and k-Homomorphisms of Gamma Rings: Jordan k-Derivations, Jordan Left/Right and Generalized k-Derivations, Jordan k-Homomorphisms and anti-k-Homomorphisms
Couverture souple
ISBN 10 : 365917839X ISBN 13 : 9783659178399
Editeur : LAP LAMBERT Academic Publishing, 2012

Synopsis

The notion of a gamma ring is a generalization of the concept of a classical ring. This attempt characterizes certain gamma rings with various types of k-derivations and k-homomorphisms. We determine the commutativity of prime gamma rings of characteristic not equal to 2 and 3 with k-derivations, left (and right) k-derivations and generalized k-derivations. We prove that every Jordan k-derivation (also, Jordan generalized k-derivation) of a gamma ring is a k-derivation (generalized k-derivation) of the same, if we consider the gamma ring as a (2-torsion free) prime, completely prime, semiprime, and completely semiprime gamma ring, under some suitable conditions (as necessary), respectively. On the other hand, we prove that every Jordan k-homomorphism of a gamma ring onto a 2-torsion free prime (also, completely prime) gamma ring is either a k-homomorphism or an anti-k-homomorphism. The analogous result is also proved for Jordan k-isomorphism of a gamma ring onto a 2-torsion free prime/completely prime gamma ring. Finally, we investigate what does happen if a k-derivation acts as a k-endomorphism and also as an anti-k-endomorphism of certain gamma rings and look what we have here.

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

Présentation de l'éditeur

The notion of a gamma ring is a generalization of the concept of a classical ring. This attempt characterizes certain gamma rings with various types of k-derivations and k-homomorphisms. We determine the commutativity of prime gamma rings of characteristic not equal to 2 and 3 with k-derivations, left (and right) k-derivations and generalized k-derivations. We prove that every Jordan k-derivation (also, Jordan generalized k-derivation) of a gamma ring is a k-derivation (generalized k-derivation) of the same, if we consider the gamma ring as a (2-torsion free) prime, completely prime, semiprime, and completely semiprime gamma ring, under some suitable conditions (as necessary), respectively. On the other hand, we prove that every Jordan k-homomorphism of a gamma ring onto a 2-torsion free prime (also, completely prime) gamma ring is either a k-homomorphism or an anti-k-homomorphism. The analogous result is also proved for Jordan k-isomorphism of a gamma ring onto a 2-torsion free prime/completely prime gamma ring. Finally, we investigate what does happen if a k-derivation acts as a k-endomorphism and also as an anti-k-endomorphism of certain gamma rings and look what we have here.

Biographie de l'auteur

Sujoy Chakraborty was born in 1972 in Comilla, Bangladesh. He earned the M.Sc. degree in Pure Mathematics in 1993 and the M.Phil. degree in 2002 at the University of Dhaka. He was awarded the Ph.D. degree in 2010 for this dissertation at the University of Rajshahi. He has been teaching at Shahjalal University of Science and Technology since 1999.

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

Éditeur
LAP LAMBERT Academic Publishing
Date d'édition
2012
Langue
anglais
ISBN 10 
365917839X
ISBN 13 
9783659178399
Reliure
Broché
Nombre de pages
128
Coordonnées du fabricant
non disponible
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