On strongly n-regular and strongly regular rings

Author

• Huey Voon Chen, Universiti Malaya

Date of Award

1-1-2000

Thesis Type

Masters

Document Type

Thesis

Divisions

Faculty of Science

Department

Institute of Mathematical Sciences

Institution

Universiti Malaya

Abstract

Let R be an associative ring with identity 1 (not equal to) 0. An element x E R is said to be right (or left) regular if there exists yin R such that x² y = x (or y.x² = x). If x is both left and right regular, then it is said to be strongly regular. The ring R is said to be strongly regular if every element of R is strongly regular. We say that x is a left -π-regular element if there exist an integer n > 0 and an element y E R such that yx n+1 = x n. A right π-regular element is defined analogously. An element of R is strongly π-regular if it is both left and right π-regular. R is strongly π-regular if every element of R is strongly π-regular. The main aim of this thesis is to study strongly regular and strongly π-regular rings. In particular, we shall be concerned with necessary and sufficient conditions for a ring to be strongly regular or strongly π-regular. We shall also study how these rings are related to other types of "regular" rings. A ring R is said to be an (s,2)-ring if every element of R is a sum of two units of R . If for any a, b E R satisfying aR ": bR = R , there exists y E R such that a + by is right invertible, then we say that R has stable range one. In a related thread, we shall study how various regular rings are related to (s,2)-rings and rings having stable range one.

Initial

snms

Additional Information

Dissertation (M.A) -- Faculty of Science, Universiti Malaya, 2001.

Recommended Citation

Chen, Huey Voon, "On strongly n-regular and strongly regular rings" (2000). Student Works (2000-2009). 86.
https://knova.um.edu.my/student_works_2000s/86

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