We Show that:(a) closures of a constructible subsets of real spectrum (Spec r A) of complete
noetherian local ring A with formally real residue field R are constructible.(b) The connected …

A topological version of Hilbert's Nullstellensatz - ScienceDirect Skip to main contentSkip to
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We determine those pairs consisting of a partially ordered set U and a collection C of
cardinal numbers which can occur as Spec (R) and the collection C (R) of cardinalities of …

The main purpose of this paper is a wide generalization of one of the results abstract
algebraic geometry begins with, namely of the fact that the prime spectrum Spec (R) Spec …

1. Introduction. Let R be a commutative ring with identity, and let A be an ideal of R.
Following the notation of Ohm and Pendleton in [4], A is called a J-radical ideal if A is an …

Much in the same way as classical algebraic varieties are generalized by the theory of
schemes, locally semi-algebraic spaces are generalized by a class of locally ringed spaces …

Real closed rings were first introduced in [48](cf.[50],[51]) for the express purpose of
establishing a new foundation for semi-algebraic geometry. The basic idea is to start with …

We present here some applications of the theory of real spectra of excellent rings to the ring
of global analytic, functions on a compact real analytic manifold. Section 1 contains the facts …

Let A be a commutative ring with identity. We extend the concept of valuation ring from fields
to rings. Then we define the Riemann surface of a ring as a topological space whose points …

This thesis has as its motivation the exploration, on an informal level, of a correspondence
between Algebra and Topology. Specifically, it considers the prime spectrum of a ring, that …