Ring in which every element is sum of two 6-potent elements

Document Type : Research Paper

Authors

1 Dept of Mathematics, Gauhati University

2 Dept. of Mathematics, Gauhati University, Guwahati-781014, Assam, India

Abstract

In this paper we prove the following results. Every element of a ring R is a sum of two
commuting 6-potent elements if and only if R is isomorphic to R_1×R_2×R_3, where R_1
is isomorphic to a subdirect product of Z_2's, R_2 is isomorphic to a subdirect product
of Z_3's and R_3 is isomorphic to a subdirect product of Z_11's. Also if every element of
a ring R is sum of two 6-potent and one nilpotent all commute each other then R is
isomorphic to R_1×R_2×R_3, where J(R_1) is nil and R_1/J(R_1) is a subdirect product of
rings isomorphic to either of the rings Z_2, F_4, M_2(F_2) and M_2(F_4), a^{81}-a is nilpotent
for every a in R2 , J(R_3) is nil and R_3/J(R_3) is a subdirect product of Z_11's.

Keywords

Journal of Algebra and Related Topics

Articles in Press, Accepted Manuscript
Available Online from 04 December 2024

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