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Graded π-rings

Published online by Cambridge University Press:  20 November 2018

D. D. Anderson  and
J. Matijevic
D. D. Anderson
Affiliation:
The University of Iowa, Iowa City, Iowa
J. Matijevic
Affiliation:
University of Southern California, Los Angeles, California
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All rings considered will be commutative with identity. By a graded ring we will mean a ring graded by the non-negative integers.

A ring R is called a π-ring if every principal ideal of R is a product of prime ideals. A π-ring without divisors of zero is called a π-domain. A graded ring (domain) is called a graded π-ring (-domain) if every homogeneous principal ideal is a product of homogenous prime ideals. A ring R is called a general ZPl-ring if every ideal is a product of primes. A graded ring is called a graded general ZPl-ring if every homogenous ideal is a product of homogeneous prime ideals.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 31 , Issue 3 , 01 June 1979 , pp. 449 - 457
Copyright
Copyright © Canadian Mathematical Society 1979

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