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A generalisation of Divinsky's radical

Published online by Cambridge University Press:  18 May 2009

F. A. Bostock  and
E. M. Patterson
F. A. Bostock
Affiliation:
The University Aberdeen
E. M. Patterson
Affiliation:
The University Aberdeen
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Let A be an associative ring. Given a ∊ A, an element b ∊ A is called a left identity for a if

Given a subset S of A, an element b ∊ A is, called a left identity for S if (1) is satisfied for all a ∊ S. An element of A need not have a left identity; for example, if A is nilpotent then no non-zero element of A has a left identity. If a does have a left identity, the latter need not be unique; if every element of a subset S of A has a left identity, then it is not necessarily true that S has a left identity.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 6 , Issue 2 , July 1963 , pp. 75 - 87
Copyright
Copyright © Glasgow Mathematical Journal Trust 1963

References

REFERENCES

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