Generalized E-rings

PETER V. DANCHEV

Author(s)

PETER V. DANCHEV Institute of Mathematics and Informatics, Bulgarian Academy of Sciences "Acad. G. Bonchev" str., bl. 8, 1113 So¯a, Bulgaria.

Abstract

Let R be a ring with center C(R). A ring R is called a »ring if, for any element x 2 R, there exists an element y 2 R such that x ¡ x2y 2 C(R). In Proc. Japan Acad. Sci., Ser. A { Math. (1957), Utumi describes the structure of these rings as a natural generalization of the classical strongly regular rings, that are rings for which x = x2y. In order to make up a natural connection of »-rings with the more general class of von Neumann regular rings, that are rings for which x = xyx, we introduce here the so-called generalized »-rings as those rings in which x ¡ xyx 2 C(R). Several characteristic properties of this newly de¯ned class are proved, which extend the corresponding ones established by Utumi in these Proceedings (1957).

Publication Details

Page(s) 13-17

DOI DOI not available

Published Journal: Journal of Prime Research in Mathematics, Volume: 14, Issue: 1, Year: 2018

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Keywords

16E50, strongly regular rings, nipotents, 13B99, 16U99, idempotents, »-rings AMS SUBJECT, regular rings

References

Arens R.,I. R. .1948 .Kaplansky: Topological representation of algebras. Trans. Amer. Math. Soc, 457 : 481.

Danchev P.V. . .A generalization of ¼-regular rings. , : .

Drazin M.P. . .: Rings with central idempotent or nilpotent elements. Proc. Edinburgh Math. Soc. 9, 157(1958) : 165.

Goodearl K.R.,Pitman K.R. .1979 .: von Neumann Regular Rings, Monographs and. Publishing Program), 4 : .

Herstein I.N. .1951 .A generalization of a theorem of Jacobson, Amer. , 755 : 762.

I.N. .1953 .Herstein: The structure of a certain class of rings, Amer. , 864 : 871.

W.S. Martindale: . .The structure of a special class of rings. Proc. Amer. Math. Soc. 9, 714(1958) : 721.

McLaughein J.,A. J. . .Rosenberg: Zero divisors and commutativity of rings. Proc. Amer. Math. Soc. 4, 203(1953) : 212.

Tuganbaev A. .2002 .. Mathematics and Its Applications, 545 : .

Utumi Y.,Ser Y. .1957 .-rings. Proc. Jap, 63 : 66.

J. von Neumann .1936 .On regular rings. Proc. Nat. Acad. Sci. USA, 101 : 108.