Results 1 to 10 of about 7,878 (33)
Non-compact subsets of the Zariski space of an integral domain [PDF]
, 2016 Let $V$ be a minimal valuation overring of an integral domain $D$ and let $\mathrm{Zar}(D)$ be the Zariski space of the valuation overrings of $D$. Starting from a result in the theory of semistar operations, we prove a criterion under which the set ...
Spirito, Dario
core +2 more sources
Big Cohen-Macaulay Algebras and Seeds [PDF]
, 2007 We delve into the properties possessed by algebras, which we have termed seeds, that map to big Cohen-Macaulay algebras. We will show that over a complete local domain of positive characteristic any two big Cohen-Macaulay algebras map to a common big ...
Dietz, Geoffrey D.
core +2 more sources
A family of quotients of the Rees algebra [PDF]
, 2014 A family of quotient rings of the Rees algebra associated to a commutative ring is studied. This family generalizes both the classical concept of idealization by Nagata and a more recent concept, the amalgamated duplication of a ring.
Barucci, Valentina +2 more
core +1 more source
On Semiprime Noetherian PI-Rings [PDF]
, 2000 Let R be a semiprime Noetherian PI-ring and Q(R) the semisimple Artinian ring of fractions of R. We shall prove the following conditions are equivalent: (1) the Krull dimention of R is at most one, (2) Any ring between R and Q(R) is again right ...
Chiba, Katsuo
core +1 more source
Topological properties of semigroup primes of a commutative ring
, 2017 A semigroup prime of a commutative ring $R$ is a prime ideal of the semigroup $(R,\cdot)$. One of the purposes of this paper is to study, from a topological point of view, the space $\scal(R)$ of prime semigroups of $R$.
Finocchiaro, Carmelo A. +2 more
core +1 more source
On the existence of maximal orders
, 2011 We generalize the existence of maximal orders in a semi-simple algebra for general ground rings. We also improve several statements in Chapter 5 and 6 of Reiner's book concerning separable algebras by removing the separability condition, provided the ...
Yu, Chia-Fu
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Properties of chains of prime ideals in an amalgamated algebra along an ideal
, 2010 Let $f:A \to B$ be a ring homomorphism and let $J$ be an ideal of $B$. In this paper, we study the amalgamation of $A$ with $B$ along $J$ with respect to $f$ (denoted by ${A\Join^fJ}$), a construction that provides a general frame for studying the ...
D'Anna, Marco +2 more
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Specialization and Integral Closure
, 2014 We prove that the integral closedness of any ideal of height at least two is compatible with specialization by a generic element. This opens the possibility for proofs using induction on the height of an ideal.
Hong, J., Ulrich, B.
core +1 more source
Liftable derivations for generically separably algebraic morphisms of schemes
, 2006 We consider dominant, generically algebraic, and tamely ramified (if the characteristic is positive) morphisms $\pi: X/S \to Y/S$, where Y,S are Noetherian and integral and X is a Krull scheme (e.g.
Källström, Rolf
core +4 more sources
Integer-valued polynomials over matrices and divided differences
, 2013 Let $D$ be an integrally closed domain with quotient field $K$ and $n$ a positive integer. We give a characterization of the polynomials in $K[X]$ which are integer-valued over the set of matrices $M_n(D)$ in terms of their divided differences.
Peruginelli, Giulio
core +3 more sources