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Ijraset Journal For Research in Applied Science and Engineering Technology

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Result Obtained in the learn of Generalized Derivations of Prime Rings

Authors: Mrs. Shubhi Agrawal, Dr. Jyotsna Chandel

DOI Link: https://doi.org/10.22214/ijraset.2022.47093

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Abstract

In this subsection, we will assume that R is a prime ring that H is a generalization of R, that L is a noncentral Lie idyllic of R, and that 0???R. If s, t ? 0 and n > 0, then for all u in L, aus(H(u)n)u(t) must equal 0. All of them fit neatly inside the specified ranges of integers. H(x) = bx for every x ? R if and only if s = 0 and b = 0; this is not the case if R satisfy s4, the normal uniqueness in four variables. In this context, b stands for the Utumi quotient ring of the right side of R. The set R is said to meet the S4 condition if and only if the function H(x) is equal to bx. Once s is equal to zero, H(x) equals bx for every x in R. It follows that H = 0 if and only if s > 0 and R does not meet S4 the requirement.

Introduction

References

[1] Albert A. A. and Muckenhoupt, B. On matrices of trace zero Michigan J. Math. 1, 1-3, 1957. [2] Beidar, K. I., Martindale W. S. and Mikhalev, A. V. Rings with Generalized Identities, Marcel Dekker, New York-Basel-Hong Kong, 1996. [3] B. Zalar, On centralizer of semiprime rings, Comment. Math. Univ. Car- olinae, 32 (1991), 609-614. [4] Erickson, T. S., Martindale, WS. and Osborn, J. M. Prime nonassociative algebras, Paci_c J. Math. 60 (1), 49-63, 1975. [5] Faith, C. and Utumi, Y. On a new proof of Lito_\'s theorem, Acta Math. Acad. Sci. Hung. 14, 369-371, 1963. [6] Jacobson, N. Structure of Rings, Amer. Math. Soc. Colloq. Pub., 37, Amer. Math. Soc., Providence, RI, 1964. [7] Lee, T. K. Generalized derivations of left faithful rings, Comm. Algebra 27, 4057-4073, 1999. [8] Lee, T. K. Lee and Shiue, W. K. Identities with generalized derivations, Comm. Algebra 29, 4437-4450, 2001. [9] M. Bresar and J. Vukman, On some additive mappings in rings with involution, Aequationes Math., 38 (1989), 178-185. https://doi.org/10.1007/bf01840003 [10] Wang, Y. Annihilator conditions with generalized derivations in prime rings, Bull. Korean Math. Soc. 48, 917-922, 2011.

Copyright

Copyright © 2022 Mrs. Shubhi Agrawal, Dr. Jyotsna Chandel . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

ijraset47093

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Authors : Mrs. Shubhi Agrawal

Paper Id : IJRASET47093

Publish Date : 2022-10-16

ISSN : 2321-9653

Publisher Name : IJRASET

DOI Link : Click Here

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