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1. CMB 2010 (vol 53 pp. 639)

Coykendall, Jim; Dutta, Tridib
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)

Mimouni, Abdeslam
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)

Kim, Hwankoo
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)

Anderson, David F.; Dobbs, David E.
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

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