منابع مشابه
Coherence in amalgamated algebra along an ideal
Let $f: Arightarrow B$ be a ring homomorphism and let $J$ be an ideal of $B$. In this paper, we investigate the transfer of the property of coherence to the amalgamation $Abowtie^{f}J$. We provide necessary and sufficient conditions for $Abowtie^{f}J$ to be a coherent ring.
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In this paper, we will show a reduction of ideal arithmetic, or more generally, of arithmetic of ZZ{modules of full rank in orders of number elds to problems of linear algebra over ZZ=mZZ, where m is a possibly composite integer. The problems of linear algebra over ZZ=mZZ will be solved directly, instead of either \reducing" them to problems of linear algebra over ZZ or factoring m and working ...
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We introduce a generalization of the Hermite normal form for matrices over a principal ideal ring R which may contain zero divisors. That normal form allows us to solve the following basic linear algebra problems. Equality decision, containment test and element test for submodules of R k , k 2 IN. The determination of images, kernels, and inverse images of homomorphisms ' : R l ! R k , l; k 2 I...
متن کاملcoherence in amalgamated algebra along an ideal
let $f: arightarrow b$ be a ring homomorphism and let $j$ be an ideal of $b$. in this paper, we investigate the transfer of the property of coherence to the amalgamation $abowtie^{f}j$. we provide necessary and sufficient conditions for $abowtie^{f}j$ to be a coherent ring.
متن کاملLinear Algebra . A publication of the International Linear Algebra Society
Nonnegative nilpotent lower triangular completions of a nonnegative nilpotent matrix are studied. It is shown that for every natural number between the index of the matrix and its order, there exists a completion that has this number as its index. A similar result is obtained for the rank. However, unlike the case of complex completions of complex matrices, it is proved that for every nonincrea...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1931
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1931-05183-1