Journal of the
Korean Mathematical Society JKMS

It is well known that for a Krull domain $R$, the divisor class group of $R$ is a torsion group if and only if every subintersection of $R$ is a ring of quotients. Thus a natural question is that under what conditions, for a non-Krull domain $R$, every ($t$-)subintersection (resp., $t$-linked overring) of $R$ is a ring of quotients or every ($t$-)subintersection (resp., $t$-linked overring) of $R$ is flat. To address this question, we introduce the notions of $*$-compact packedness and $*$-coprime packedness of (an ideal of) an integral domain $R$ for a star operation $*$ of finite character, mainly $t$ or $w$. We also investigate the $t$-theoretic analogues of related results in the literature.

Keywords: $t$-coprimely packed, $t$-compactly packed, strong Mori domain, Pr\"ufer $v$-multiplication domain, $tQR$-property, ($t$-)flat

MSC numbers: Primary 13A15