let $(r,m)$ be a commutative noetherian local ring, $m$ a finitely generated $r$-module of dimension $d$, and let $i$ be an ideal of definition for $m$. in this paper, we extend cite[corollary 10(4)]{p} and also we show that if $m$ is a cohen-macaulay $r$-module and $d=2$, then $lambda(frac{widetilde{i^nm}}{jwidetilde{i^{n-1}m}})$ does not depend on $j$ for all $ngeq 1$, where $j$ is a minimal ...

the submodules with the property of the title ( a submodule $n$ of an $r$-module $m$ is called strongly dense in $m$, denoted by $nleq_{sd}m$, if for any index set $i$, $prod _{i}nleq_{d}prod _{i}m$) are introduced and fully investigated. it is shown that for each submodule $n$ of $m$ there exists the smallest subset $d'subseteq m$ such that $n+d'$ is a strongly dense submodule of $m$...

0. Short Abstract The syntax of Control structures like They love to swim. has long been a topic of debate. Current generative treatments of such sentences, as in, e.g., Baltin (1995), Bo kovi (1996, 2007), Chomsky & Lasnik (1993, 1995), Landau (2004, 2008), Sigur sson (2008), among others, continue to analyze them in terms of a phonetically non-overt, non-expletive, pronominal (PRO) in the sub...

Opinions differ on whether the readings in [1] are semantically distinct, or are pragmatic interpretations of a basic perfect meaning. The popular Reichenbachian theory of tense and aspect (Reichenbach 1947; important later studies include Comrie 1976, 1985, Dowty 1982, Partee 1984, Binnick 1991, Hornstein 1990, Kamp & Reyle 1993, Klein 1994) seems to force the latter view, for it provides an u...