Volume 68 | Issue 3 | Year 2022 | Article Id. IJMTT-V68I3P511 | DOI : https://doi.org/10.14445/22315373/IJMTT-V68I3P511
Let R bearing with unity and satisfying certain conditions, for all 𝑥, 𝑦 ∈ 𝑅. In this paper, we extend a well known result.
[1] Abu-Khuzam, H., H. Bell, A. Yaqub, Commutativity of Rings Satisfying Certain Polynomial Identities, Bull. Austral. Math. Soc., 44 (1991) 63-69
[2] Abu-Khuzam, H., H. Tominaga, A. Yaqub, Commutativity Theorem for S-Unital Rings Satisfying Polynomial Identities, Math. J. Okayama Univ., 22 (1980) 111-114.
[3] Abu-Khuzam, H., A. Yaqub, Commutativity of Rings With No Nonzero Nil Ideals, Math. Japonica, 30(2) (1985) 165-168. [4] Bell, H.E., On The Power Map And Ring Commutativity, Canad. Math. Bull., 21(4) (1978) 399-404.
[5] Bell, H.E., On Two Commutativity Properties for Rings, Math. Japonica, 26(5) (1981) 523-528.
[6] Bell, H.E.,On Commutativity of Rings With Constrains on Commutators, Results Math., 8 (1985) 123-131.
[7] Bell, H.E., A Setwise Commutativity Property for Rings, Comm. Algebra., 25(3) (1997) 989-998.
[8] Faith,C.,Posneralgebraicdivisionextensions,Proc.Amer.Math.Soc.,110(1960) 43-53.
[9] Herstein,I.N.,Two remarks on commutativityofrings,Canad.J.Math.7(1955) 411-412.
[10] Herstein,I.N.,Two on the Hypercentreof a Ring,J. Algebra.36(1975), 151-155.
[11] Herstein,I.N.,A Commutativity Theorem,J. Algebra.38(1976) 112-115.
[12] Herstein., I. N. A Theorem on Rings, Can. J. Math., 5 (1953) 238–241.
[13] Herstein., I. N., A Generalization of a Theorem of Jacobson III, Amer. J. Math., 75 (1953)105–111.
[14] Herstein., I. N., The Structure of a Certain Class of Rings, Amer. J. Math., 75 (1953) 864–871.
[15] Herstein, I. N., A Condition for Commutativity of Rings, Canad. J. Math., 9 (1957) 583-586.
[16] Herstein, I. N., Non-Commutative Rings, Cyrus Monograph No. 15, Math. Association of America, Washington, D.C., (1968).
[17] Herstein, I. N., On the Hypercenter of A Ring, J. Algebra, 36(1975)151-155.
[18] Jacobson, N., Structure of Rings Amer. Math. Soc. Coll. Pub. (1956).
[19] Kezlan, T. P., On Identities Which Are Equivalent With Commutativity, Math. Japonica, 29 (1) (1984) 135-139
[20] Kezlan, T. P., On Identities Which Are Equivalent With Commutativity II, Math. Japonica, 34 (2) (1989) 197-204
[21] Klein, A., I. Nada, H.E. Bell, Some Commutativity Results for Rings, Bull. Austral. Math. Soc., 22 (1980) 285-289.
[22] Luh, J., A Commutativity Theorem for Primary Rings, Acta Math. Acad. Sci. Hungar., 22 (1977) 75-77.
[23] Lihtman, A. I., Rings that are Radical over Commutative Subrings, Mat. Shornik. 83 (1970) 513-523.
[24] Outcalt, ., A. Yaqub, A Commutativity Theorem for Rings With Constraints Involving An Additive Subsemigroup, Math. Japonica, 24 (2) (1979) 195-202
[25] Psomopoulos, E., A Commutativity Theorem for Rings, Math. Japonica, 29 (3) (1984) 371-373.
Rekha Rani, "An Extension of a Theorem of Herstein," International Journal of Mathematics Trends and Technology (IJMTT), vol. 68, no. 3, pp. 59-62, 2022. Crossref, https://doi.org/10.14445/22315373/IJMTT-V68I3P511