منابع مشابه
On radical formula and Prufer domains
In this paper we characterize the radical of an arbitrary submodule $N$ of a finitely generated free module $F$ over a commutatitve ring $R$ with identity. Also we study submodules of $F$ which satisfy the radical formula. Finally we derive necessary and sufficient conditions for $R$ to be a Pr$ddot{mbox{u}}$fer domain, in terms of the radical of a cyclic submodule in $Rbigopl...
متن کاملon radical formula and prufer domains
in this paper we characterize the radical of an arbitrary submodule $n$ of a finitely generated free module $f$ over a commutatitve ring $r$ with identity. also we study submodules of $f$ which satisfy the radical formula. finally we derive necessary and sufficient conditions for $r$ to be a pr$ddot{mbox{u}}$fer domain, in terms of the radical of a cyclic submodule in $rbigopl...
متن کاملOn a Depth Formula for Modules over Local Rings
We prove that for modules M and N over a local ring R, the depth formula: depthR M + depthR N − depthR = depthR Tor R s (M,N) − s, where s = sup{i | Tor i (M,N) 6= 0}, holds under certain conditions. This adds to the list cases where the depth formula, which extends the classical Auslander-Buchsbaum equality, is satisfied.
متن کاملA Weight Multiplicity Formula for Demazure Modules
We establish a formula for the weight multiplicities of Demazure modules (in particular for highest weight representations) of a complex connected algebraic group in terms of the geometry of its Langlands dual.
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ژورنال
عنوان ژورنال: Glasgow Mathematical Journal
سال: 2011
ISSN: 0017-0895,1469-509X
DOI: 10.1017/s0017089511000243