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...
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Since the theory of ideals plays an important role in the theory of quotient semirings, in this paper, we will make an intensive study of the notions of Noetherian, Artinian, prime, primary, weakly primary and k-maximal ideals in commutative quotient semirings. The bulk of this paper is devoted to stating and proving analogues to several well-known theorems in the theory of the residue class ri...
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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...
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The rings considered in this article are commutative rings with identity $1neq 0$. The aim of this article is to define and study the exact annihilating-ideal graph of commutative rings. We discuss the interplay between the ring-theoretic properties of a ring and graph-theoretic properties of exact annihilating-ideal graph of the ring.
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This paper advances a framework to conceptualize societal caregiving arrangements abstractly. It is abstract in that it brackets the meaning of our particular relationships. This framework, which I call the arrow of care map, is a descriptive tracking model that is a necessary component of a theory of justice, but it is not a normative prescription in itself. The basic idea of the map is then m...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1962
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1962.12.481