Ring extensions with some finiteness conditions on the set of intermediate rings

extensions of some polynomial inequalities to the polar derivative

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On Chains of Intermediate Rings Resulting from the Juxtaposition of Minimal Ring Extensions

Let R ⊂ S and S ⊂ T be minimal ring extensions of (commutative) rings. If (i) each of these extensions is integral or (ii) each of these extensions is integrally closed or (iii) R ⊂ S is integral while S ⊂ T is integrally closed, then each chain of rings between R and T is finite. Examples are given of minimal extensionsR ⊂ S and S ⊂ T such thatR ⊂ S is integrally closed, S ⊂ T is any of the th...

the effect of taftan pozzolan on the compressive strength of concrete in the environmental conditions of oman sea (chabahar port)

cement is an essential ingredient in the concrete buildings. for production of cement considerable amount of fossil fuel and electrical energy is consumed. on the other hand for generating one tone of portland cement, nearly one ton of carbon dioxide is released. it shows that 7 percent of the total released carbon dioxide in the world relates to the cement industry. considering ecological issu...

SOME FINITENESS CONDITIONS ON THE SET OF t-LINKED OVERRINGS OF AN INTEGRAL DOMAIN

Let R be an integral domain with quotient field L. An overring T of R is t-linked over R if I = R implies that (T : IT ) = T for each finitely generated ideal I of R. Let Ot(R) denotes the set of all t-linked overrings of R and O(R) the set of all overrings of R. The purpose of this paper is to study some finiteness conditions on the set Ot(R). Particularly, we prove that if Ot(R) is finite, th...

Some Finiteness Conditions on the Set of Overrings of an Integral Domain