International Journal of Advanced Research and Publications (2456-9992)

High Quality Publications & World Wide Indexing!

Some Characterizations of Lie And Jordan Ideals of Gamma Rings With Involution

Volume 6 - Issue 2, February 2023 Edition
[Download Full Paper]

Md. Sabur Uddin; Md. Zakaria Hossain
Centre of a gamma ring, Involution gamma ring, Lie and Jordan ideals, Semi-prime gamma rings.
In this article, we have developed some characterizations of Lie and Jordan ideals of simple and semi-prime gamma rings by means of involution mapping. Several properties of arbitrary gamma rings related to this work are also established here.
[1]. R Awtar, On Jordan Structure in Semi-prime Rings, Can. J. Math., vol. 28, no. 5, 1067-1072, 1976 .

[2]. W.E. Barnes, On the gamma rings of Nobusawa, Pacific J. Math, vol. 18, no. 3, 411-422, 1966.

[3]. P.M. Cohn, Prime rings with involution whose symmetric zero-divisors are nilpotent, Proc. AMS., vol. 40, no. 1, 91-92, 1973.

[4]. R.K.H. Ibraheem and A. H. Majeed, On Lie Structure in Semi-prime Inverse Semi-rings, Iraqi Journal of Science vol. 60, No.12, 2711-2718, 2019.

[5]. I.N.Herstein, Topics in Ring Theory, The University of Chicago Press, 1969.

[6]. I.N.Herstein, Rings with Involution, The university of Chicago press Chicago and London,1976.

[7]. C. Lanski, Rings with involution whose symmetric elements are regular, Proc. AMS., Vol. 33, no. 2, 264- 270, 1972.

[8]. S. Montgomery, Rings with involution in which every trace is nilpotent or regular, Canadian Math. Jour. Vol. 26, no. 1, 130-137, 1974.

[9]. N. Nobusawa , On a generalization of the ring theory, Osaka J. Math. Vol. 1, no. 1, 81-89, 1964.

[10]. A.C.Paul and S. Uddin, Lie and Jordan Structure in Simple Gamma Rings, Journal of Physical Sciences, vol. 14, 77-86, 2010.

[11]. A.C. Paul and S. Uddin, Lie Structure in Simple Gamma Rings, International Journal of Pure and Applied Sciences and Technology vol. 4, no. 2, 63-70, 2010.

[12]. A.C.Paul and S. Uddin, ” Simple Gamma Rings with involutions” International Organization of Scientific Research Journal of Mathematics (IOSR-JM) vol. 4, no. 3, 40-48, 2012.

[13]. A.C.Paul and S. Uddin, Lie Structure in Simple Gamma Rings with Involution, Journal of the Calcutta Mathematical Society vol.9, no. 2, 87-100, 2013