JP Journal of Algebra, Number Theory and Applications
Volume 4, Issue 2, Pages 337 - 351
(August 2004)
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STRONGLY
PRIME IDEALS, SUPER DIVIDED IDEALS, SUPER
POWERFUL IDEALS, AND VALUATION DOMAINS
Akira Okabe (Japan)
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Abstract: In [Pacific J. Math. 67
(1976), 353-363] the notion of a divided ideal
was introduced and in [Comm. Algebra 30 (2002),
1591-1606] the notion of a powerful ideal
was introduced. In this paper we introduce two
new notions of a super divided ideal and
a super powerful ideal as generalizations of the
above two notions. For a prime ideal P of
an integral domain D, we show that P is
strongly prime iff P is super divided iff
P is super powerful. By the use of
powerful ideals we shall give some new
characterizations of a valuation domain. |
Keywords and phrases: strongly prime, super
divided, super powerful, pseudo-valuation domain. |
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