1,720,991 research outputs found
Cancellation properties in ideal systems: a classification of e.a.b. semistar operations
No full textWe give a classification of e.a.b. semistar (and star) operations by defining four different (successively smaller) distinguished classes. Then, using a standard notion of equivalence of semistar (and star) operations to partition the collection of all e.a.b. semistar (or star) operations, we show that there is exactly one operation
of finite type in each equivalence class and that this operation has a range of nice properties. We give examples to demonstrate that the four classes of e.a.b. semistar (or star) operations we defined can all be distinct. In particular, we solve the open problem
of showing that a.b. is really a stronger condition than e.a.b
An ultrapower analogue of the Kronecker function ring
Full text linkWe introduce an analogue of the Kronecker function ring construction in the ultrapower setting, and study when it gives a Bézout domain
The patch topology and the ultrafilter topology on the prime spectrum of a commutative ring
No full textLet R be a commutative ring and let Spec R denote the collection of prime ideals of R. We define a topology on Spec R by using ultrafilters and demonstrate that this topology is identical to the well-known patch or constructible topology. The proof is
accomplished by use of a von Neumann regular ring canonically associated with R
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