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1. CMB 2010 (vol 53 pp. 639)
A Generalization of Integrality
In this paper, we explore a generalization of the notion of
integrality. In particular, we study a near-integrality condition that is
intermediate between the concepts of integral and almost integral.
This property (referred to as the $\Omega$-almost integral
property) is a representative independent specialization of the
standard notion of almost integrality. Some of the properties of
this generalization are explored in this paper, and these properties
are compared with the notion of pseudo-integrality introduced by
Anderson, Houston, and Zafrullah. Additionally, it is
shown that the $\Omega$-almost integral property serves to
characterize the survival/lying over pairs of Dobbs and Coykendall
Keywords:integral closure, complete integral closure Categories:13B22, 13G05, 13B21 |
2. CMB 2008 (vol 51 pp. 406)
Condensed and Strongly Condensed Domains This paper deals with the concepts of condensed and strongly condensed
domains. By definition, an integral domain $R$ is condensed
(resp. strongly condensed) if each pair of ideals $I$ and $J$ of $R$,
$IJ=\{ab/a \in I, b \in J\}$ (resp. $IJ=aJ$ for some $a \in I$ or
$IJ=Ib$ for some $b \in J$). More precisely, we investigate the
ideal theory of condensed and strongly condensed domains in
Noetherian-like settings, especially Mori and strong Mori domains and
the transfer of these concepts to pullbacks.
Categories:13G05, 13A15, 13F05, 13E05 |
3. CMB 2000 (vol 43 pp. 362)
Examples of Half-Factorial Domains In this paper, we determine some sufficient conditions for an $A +
XB[X]$ domain to be an HFD. As a consequence we give new examples
of HFDs of the type $A + XB[X]$.
Keywords:atomic domain, HFD Categories:13A05, 13B30, 13F15, 13G05 |
4. CMB 1998 (vol 41 pp. 3)
Root closure in Integral Domains, III {If A is a subring of a commutative ring B and if n
is a positive integer, a number of sufficient conditions are given for
``A[[X]]is n-root closed in B[[X]]'' to be equivalent to ``A is n-root
closed in B.'' In addition, it is shown that if S is a multiplicative
submonoid of the positive integers ${\bbd P}$ which is generated by
primes, then there exists a one-dimensional quasilocal integral domain
A (resp., a von Neumann regular ring A) such that $S = \{ n \in {\bbd P}\mid
A$ is $n$-root closed$\}$ (resp., $S = \{n \in {\bbd P}\mid A[[X]]$
is $n$-rootclosed$\}$).
Categories:13G05, 13F25, 13C15, 13F45, 13B99, 12D99 |