منابع مشابه
Commutative Ideal Theory without Finiteness Conditions: Primal Ideals
Our goal is to establish an efficient decomposition of an ideal A of a commutative ring R as an intersection of primal ideals. We prove the existence of a canonical primal decomposition: A = ⋂ P∈XA A(P ), where the A(P ) are isolated components of A that are primal ideals having distinct and incomparable adjoint primes P . For this purpose we define the set Ass(A) of associated primes of the id...
متن کاملCommutative Ideal Theory without Finiteness Conditions: Completely Irreducible Ideals
An ideal of a ring is completely irreducible if it is not the intersection of any set of proper overideals. We investigate the structure of completely irrreducible ideals in a commutative ring without finiteness conditions. It is known that every ideal of a ring is an intersection of completely irreducible ideals. We characterize in several ways those ideals that admit a representation as an ir...
متن کاملFiniteness of certain local cohomology modules
Cofiniteness of the generalized local cohomology modules $H^{i}_{mathfrak{a}}(M,N)$ of two $R$-modules $M$ and $N$ with respect to an ideal $mathfrak{a}$ is studied for some $i^{,}s$ witha specified property. Furthermore, Artinianness of $H^{j}_{mathfrak{b}_{0}}(H_{mathfrak{a}}^{i}(M,N))$ is investigated by using the above result, in certain graded situations, where $mathfrak{b}_{0}$ is an idea...
متن کاملCommutative Ideal Theory without Finiteness Conditions: Irreducibility in the Quotient Field
Let R be an integral domain and let Q denote the quotient field of R. We investigate the structure of R-submodules of Q that are Q-irreducible, or completely Q-irreducible. One of our goals is to describe the integral domains that admit a completely Q-irreducible ideal, or a nonzero Q-irreducible ideal. If R has a nonzero finitely generated Q-irreducible ideal, then R is quasilocal. If R is int...
متن کاملToeplitz transforms of Fibonacci sequences
We introduce a matricial Toeplitz transform and prove that the Toeplitz transform of a second order recurrence sequence is another second order recurrence sequence. We investigate the injectivity of this transform and show how this distinguishes the Fibonacci sequence among other recurrence sequences. We then obtain new Fibonacci identities as an application of our transform.
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1980
ISSN: 0021-8693
DOI: 10.1016/0021-8693(80)90031-9