Results 141 to 150 of about 474 (163)

STRONGLY SEMIPRIME AND STRONGLY NILPOTENT IDEALS

JP Journal of Algebra, Number Theory and Applications, 2016
In the paper under review, the author introduces the notion of ``strongly semiprime ideals'' and it is shown that an ideal is a strongly semi prime ideal if and only if it is intersection of strongly prime ideals.
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Localization of Right Noetherian Rings at Semiprime Ideals

Canadian Journal of Mathematics, 1974
In [11] and [12] we investigated the process of localization of right Noetherian rings R at prime ideals. We shall now extend these investigations to semiprime ideals N of R.In Section 2 we show that localizing at the injective right R-module E(R/N) is the same as localizing with respect to the multiplicative ...
Lambek, J., Michler, G.
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PRIME AND SEMIPRIME BI-IDEALS

Quaestiones Mathematicae, 1983
Abstract Prime and semiprime bi-ideals in associative rings are defined. This provides a setting for a generalization of the well-known theorem that a commutative ring is Von Neumann regular iff every ideal is semiprime.
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ON GRADED SEMIPRIME AND GRADED WEAKLY SEMIPRIME IDEALS

2013
Let G be an arbitrary group with identity e and let R be a G-graded ring. In this paper, we define graded semiprime ideals of a commutative G-graded ring with nonzero identity and we give a number of results concerning such ideals. Also, we extend some results of graded semiprime ideals to graded weakly semiprime ideals.
FARZALİPOUR, Farkhonde, GHİASVAND, Peyman   +1 more
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Graded S-semiprime ideals and graded weakly S-semiprime ideals of graded rings

Asian-European Journal of Mathematics
Let [Formula: see text] be a graded ring and [Formula: see text] be a multiplicative closed subset of [Formula: see text]. In this paper, we introduce the concepts of graded [Formula: see text]-semiprime ideals and graded weakly [Formula: see text]-semiprime ideals of [Formula: see text].
Shaswati Doloi, Jituparna Goswami
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Multiplicative generalized derivations on ideals in semiprime rings

Mathematica Slovaca, 2016
Abstract Let R be a ring and I is a nonzero ideal of R. A mapping F:R → R is called a multiplicative generalized derivation if there exists a mapping g:R → R such that F(xy) = F(x)y + xg(y), for all x, y ∈ R. In the present paper, we shall prove that R contains a nonzero central ideal if any one of the following holds:
openaire   +3 more sources

Semiprime rings with D.C.C. on principal bi-ideals

Periodica Mathematica Hungarica, 1986
The main result of the paper is the equivalence of the following conditions: 1) A is a semiprime ring with d.c.c. on bi-ideals of the form aAb, a,b\(\in A\); 2) A is semiprime with d.c.c. on principal bi-ideals; 3) A is semiprime and A coincides with its right socle; 4) Every finite subset of A can be embedded in a bi-ideal of A which is semiprime ...
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Derivations on Lie ideals in semiprime rings

Rendiconti del Circolo Matematico di Palermo, 1985
The purpose of this note is to prove that if \(R\) is a 2-torsion free semiprime ring with a derivation \(D\) and Lie ideal \(U\) satisfying \(D^ 2(U)=0\), then \(D(U)\) is in the center of \(R\).
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Prime and Semiprime Ideals in Semirings

1999
As in the case of rings, an ideal I of a semiring R is prime if and only if whenever H K ⊆ I, for ideals H and K of R, we must have either H ⊆ I or K ⊆ I. The set of all prime ideals of a semiring R is called the spectrum of R and will be denoted by spec(R).
openaire   +1 more source

Note on Lie ideals with symmetric bi-derivations in semiprime rings

Indian Journal of Pure and Applied Mathematics, 2022
Emine Koc Sogutcu
exaly