UGC Approved Journal no 63975(19)

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Published in:

Volume 7 Issue 6
June-2020
eISSN: 2349-5162

UGC and ISSN approved 7.95 impact factor UGC Approved Journal no 63975

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Published Paper ID:
JETIR2006542


Registration ID:
234807

Page Number

1441-1443

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Title

ON COMMUTATIVITY FOR NON ASSOCIATIVE PRIMITIVE RINGS WITH x(x2 +y2 ) – (x2 +y2 ) x ∈ z(R)

Abstract

Johnson, Outcalt and Yaqub [3] proved that if a non- associative ring R satisfy the identity x2 y2 = y2 x2 for all x,y in R, then R is commutative. The generalization of this result proved by R. D. Giri and others [1] stoctes that if R is a non-associative primitive ring satisfies the identities x2 y2- y2 x2 ∈ z(R), where z(R) denotes the center, then R is commutative. A modification of Johnson's identity viz, x2 y2- y2 x2 for all x,y in R, for a non - associative ring R which has no element of additive order 2, is commutative was proved by R. N. Gupta [2], R. D. Giri and others [1] generalized Gupta's result by taking x(xy)2 -(xy)2 x ∈ z(R). We have to proved that if R is a non-associative ring of char≠4 satisfies then R is commutative x(x2 + y)2- (x2 + y)2 x ∈ z(R)

Key Words

Center,Commutativity,Primitive Ring.

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"ON COMMUTATIVITY FOR NON ASSOCIATIVE PRIMITIVE RINGS WITH x(x2 +y2 ) – (x2 +y2 ) x ∈ z(R)", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.7, Issue 6, page no.1441-1443, June 2020, Available :http://www.jetir.org/papers/JETIR2006542.pdf

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2349-5162 | Impact Factor 7.95 Calculate by Google Scholar

An International Scholarly Open Access Journal, Peer-Reviewed, Refereed Journal Impact Factor 7.95 Calculate by Google Scholar and Semantic Scholar | AI-Powered Research Tool, Multidisciplinary, Monthly, Multilanguage Journal Indexing in All Major Database & Metadata, Citation Generator

Cite This Article

"ON COMMUTATIVITY FOR NON ASSOCIATIVE PRIMITIVE RINGS WITH x(x2 +y2 ) – (x2 +y2 ) x ∈ z(R)", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.7, Issue 6, page no. pp1441-1443, June 2020, Available at : http://www.jetir.org/papers/JETIR2006542.pdf

Publication Details

Published Paper ID: JETIR2006542
Registration ID: 234807
Published In: Volume 7 | Issue 6 | Year June-2020
DOI (Digital Object Identifier):
Page No: 1441-1443
Country: 3RD CROSS, ANDHRAPRADESH, India .
Area: Mathematics
ISSN Number: 2349-5162
Publisher: IJ Publication


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