منابع مشابه
The Dual of a Strongly Prime Ideal
Let R be a commutative integral domain with quotient field K and let P be a nonzero strongly prime ideal of R. We give several characterizations of such ideals. It is shown that (P : P) is a valuation domain with the unique maximal ideal P. We also study when P^{&minus1} is a ring. In fact, it is proved that P^{&minus1} = (P : P) if and only if P is not invertible. Furthermore, if P is invertib...
متن کاملSOME RESULTS ON STRONGLY PRIME SUBMODULES
Let $R$ be a commutative ring with identity and let $M$ be an $R$-module. A proper submodule $P$ of $M$ is called strongly prime submodule if $(P + Rx : M)ysubseteq P$ for $x, yin M$, implies that $xin P$ or $yin P$. In this paper, we study more properties of strongly prime submodules. It is shown that a finitely generated $R$-module $M$ is Artinian if and only if $M$ is Noetherian and every st...
متن کاملPrime Radical Theory of Hemirings
Giri and Wazalwar evolved concepts of prime ideal and prime radical in noncommutative semigroups. A hemiring is a ring without subtraction (additive inverse), may not have commutativity and identity. A hemiring with identity is called a semiring. It is well known that a hemiring can be embedded in a semiring. We will use this fact to develop proofs of some results on prime radical in a hemiring...
متن کاملThe Prime Radical in Alternative Rings
The characterization by J. Levitzki of the prime radical of an associative ring R as the set of strongly nilpotent elements of R is adapted here to apply to a wide class of nonassociative rings. As a consequence it is shown that the prime radical is a hereditary radical for the class of alternative rings and that the prime radical of an alternative ring coincides with the prime radical of its a...
متن کاملsome results on strongly prime submodules
let $r$ be a commutative ring with identity and let $m$ be an $r$-module. a proper submodule $p$ of $m$ is called strongly prime submodule if $(p + rx : m)ysubseteq p$ for $x, yin m$, implies that $xin p$ or $yin p$. in this paper, we study more properties of strongly prime submodules. it is shown that a finitely generated $r$-module $m$ is artinian if and only if $m$ is noetherian and every st...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1979
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1979-0537080-8