On quasi-regularity in gamma near-rings

The Jacobson radicals, J ν , ( ν = 0 , 1 , 2 ), of Γ -near-rings were introduced and studied by Booth. In this paper quasi-regular elements in a Γ -near-ring are introduced and a characterization of the J 0 -radical of a Γ -near-ring in terms of quasi-regular ideals is given. It is also proved that...

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Bibliographic Details
Published inBeiträge zur Algebra und Geometrie Vol. 60; no. 3; pp. 527 - 535
Main Authors Ravi, Srinivasa Rao, Cheruvu, Krishnaveni
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2019
Springer Nature B.V
Subjects
Algebra
Algebraic Geometry
Convex and Discrete Geometry
Geometry
Mathematics
Mathematics and Statistics
Original Paper
Subgroups
Quasi-regular elements
Jacobson radicals of type-0, 1 and 2
Gamma near-ring
Modular left ideals of type-0, 1 and 2
16Y30
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Summary:The Jacobson radicals, J ν , ( ν = 0 , 1 , 2 ), of Γ -near-rings were introduced and studied by Booth. In this paper quasi-regular elements in a Γ -near-ring are introduced and a characterization of the J 0 -radical of a Γ -near-ring in terms of quasi-regular ideals is given. It is also proved that J 0 ( M ) is nilpotent for a Γ -near-ring M with DCC on M Γ -subgroups of M. It is verified that if M is a Γ -near-ring satisfying DCC on M Γ -subgroups of M then J 2 ( M ) = J 1 ( M ) = J 1 / 2 ( M ) = J 0 ( M ) .
ISSN:0138-4821
2191-0383
DOI:10.1007/s13366-018-0427-1