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Injective and projective Boolean-like rings

Part of: General commutative ring theory Homological algebra

Published online by Cambridge University Press:  09 April 2009

V. Swaminathan
V. Swaminathan
Affiliation:
Department of Mathematics Andhra UniversityWaltair - 530 003, India
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Abstract

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A Boolean-like ring R is a commutative ring with unity in which 2x = 0 and xy(1 + x)(1 + y) = 0 hold for all elements x, y of the ring R. It is shown in this paper that in the category of Boolean-like rings, R is injective if and only if R is a complete Boolean ring and R is projective if and only if R = {0, 1}.

Keywords

Category of Boolean-like ringsBoolean-like ringsinjective and projective objectscomplete Boolean rings.

MSC classification

Secondary: 13A99: None of the above, but in this section 18G05: Projectives and injectives
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 33 , Issue 1 , August 1982 , pp. 40 - 49
Copyright
Copyright © Australian Mathematical Society 1982

References

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