Displaying similar documents to “Dimension in algebraic frames”

Conditions under which R ( x ) and R 〈 x 〉 are almost Q-rings

Hani A. Khashan, H. Al-Ezeh (2007)

Archivum Mathematicum

Similarity:

All rings considered in this paper are assumed to be commutative with identities. A ring R is a Q -ring if every ideal of R is a finite product of primary ideals. An almost Q -ring is a ring whose localization at every prime ideal is a Q -ring. In this paper, we first prove that the statements, R is an almost Z P I -ring and R [ x ] is an almost Q -ring are equivalent for any ring R . Then we prove that under the condition that every prime ideal of R ( x ) is an extension of a prime ideal of R , the ring R ...

Minimal prime ideals of skew polynomial rings and near pseudo-valuation rings

Vijay Kumar Bhat (2013)

Czechoslovak Mathematical Journal

Similarity:

Let R be a ring. We recall that R is called a near pseudo-valuation ring if every minimal prime ideal of R is strongly prime. Let now σ be an automorphism of R and δ a σ -derivation of R . Then R is said to be an almost δ -divided ring if every minimal prime ideal of R is δ -divided. Let R be a Noetherian ring which is also an algebra over ℚ ( ℚ is the field of rational numbers). Let σ be an automorphism of R such that R is a σ ( * ) -ring and δ a σ -derivation of R such that σ ( δ ( a ) ) = δ ( σ ( a ) ) for all a ∈ R . Further,...

Isolated points and redundancy

P. Alirio J. Peña, Jorge E. Vielma (2011)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

We describe the isolated points of an arbitrary topological space ( X , τ ) . If the τ -specialization pre-order on X has enough maximal elements, then a point x ∈ X is an isolated point in ( X , τ ) if and only if x is both an isolated point in the subspaces of τ -kerneled points of X and in the τ -closure of { x } (a special case of this result is proved in Mehrvarz A.A., Samei K., , J. Sci. Islam. Repub. Iran (1999), no. 3, 193–196). This result is applied to an arbitrary subspace of the prime spectrum Spec ( R ) of...

Real holomorphy rings and the complete real spectrum

D. Gondard, M. Marshall (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

Similarity:

The complete real spectrum of a commutative ring A with 1 is introduced. Points of the complete real spectrum Sper c A are triples α = ( 𝔭 , v , P ) , where 𝔭 is a real prime of A , v is a real valuation of the field k ( 𝔭 ) : = qf ( A / 𝔭 ) and P is an ordering of the residue field of v . Sper c A is shown to have the structure of a spectral space in the sense of Hochster []. The specialization relation on Sper c A is considered. Special attention is paid to the case where the ring A in question is a real holomorphy ring.