1. 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
Noetherianlike settings, especially Mori and strong Mori domains and
the transfer of these concepts to pullbacks.
Categories:13G05, 13A15, 13F05, 13E05 

2. CMB 2003 (vol 46 pp. 3)
 Anderson, D. D.; Dumitrescu, Tiberiu

Condensed Domains
An integral domain $D$ with identity is condensed (resp., strongly
condensed) if for each pair of ideals $I$, $J$ of $D$, $IJ=\{ij; i\in I,
j\in J\}$ (resp., $IJ=iJ$ for some $i\in I$ or $IJ =Ij$ for some
$j\in J$). We show that for a Noetherian domain $D$, $D$ is condensed
if and only if $\Pic(D)=0$ and $D$ is locally condensed, while a local
domain is strongly condensed if and only if it has the twogenerator
property. An integrally closed domain $D$ is strongly condensed if and
only if $D$ is a B\'{e}zout generalized Dedekind domain with at most one
maximal ideal of height greater than one. We give a number of
equivalencies for a local domain with finite integral closure to be
strongly condensed. Finally, we show that for a field extension
$k\subseteq K$, the domain $D=k+XK[[X]]$ is condensed if and only if
$[K:k]\leq 2$ or $[K:k]=3$ and each degreetwo polynomial in $k[X]$
splits over $k$, while $D$ is strongly condensed if and only if $[K:k]
\leq 2$.
Categories:13A15, 13B22 
