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On Very Large One Sided Ideals of a Ring

Published online by Cambridge University Press:  20 November 2018

Kwangil Koh
Kwangil Koh*
Affiliation:
North Carolina State University Raleigh, North Carolina
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If R is a ring, a right (left) ideal of R is said to be large if it has non-zero intersection with each non-zero right (left) ideal of R [8]. If S is a set, let |S| be the cardinal number of S. We say a right (left) ideal I of a ring R is very large if |R/I| < < No. If a is an element of a ring R such that (a)r = {r ∊ R|ar = 0} is very large then we say a is very singular. The set of all very singular elements of a ring R is a two sided ideal of R. If R is a prime ring, then 0 is the only very singular element of R and a very large right (left) ideal of R is indeed large provided that R is not finite.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 9 , Issue 2 , June 1966 , pp. 191 - 196
Copyright
Copyright © Canadian Mathematical Society 1966

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