Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5772865 | Journal of Pure and Applied Algebra | 2017 | 37 Pages |
Abstract
Let A be a commutative ring containing the rationals. Let S be a multiplicatively closed subset such that 1âS and 0âS, T a cone in A such that SâT and I an ideal in A. ThenÏS,TI={a|sa2m+tâI2mfor some mâN,sâS and tâT} is an ideal. For a commutative ring the collection of non-reduced orders (total cones) is a fibration of the real spectrum. Both concepts carry information regarding multiple solutions in the constructible set associated with I,T and S. When the ring is a real regular domain, a non-reduced Nullstellensatz is presented that extends the real Nullstellensatz and relates these concepts. The notion of real multiplicity is proposed and examined for elements that are either positive definite (PD) or positive semi-definite (PSD) on the real spectrum.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
James McEnerney,