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Strong ring extensions andphi-pseudo-valuation rings
(University of Houston, 2006)
In this paper, we extend the concept of strong extensions of domains to the context of (commutative) rings with zero-divisors. We show that the theory of strong extensions of rings resembles that of strong extensions of domains.
On phi-Mori rings
(University of Houston, 2006)
A commutative ring R is said to be a phi-ring if its nilradical Nil(R) is both prime and comparable with each principal ideal. The name is derived from the natural map phi from the total quotient ring T(R) to R localized ...