منابع مشابه
Prime Decompositions of Radicals in Polynomial Rings
In the last twenty years several methods for computing primary decompositions of ideals in multivariate polynomial rings over fields (Seidenberg (1974), Lazard (1985), Kredel (1987), Eisenbud et al. (1992)), the integers (Seidenberg, 1978), factorially closed principal ideal domains (Ayoub (1982), Gianni et al. (1988)) and more general rings (Seidenberg, 1984) have been proposed. A related prob...
متن کاملUnitary Strongly Prime Rings and Related Radicals
A unitary strongly prime ring is defined as a prime ring whose central closure is simple with identity element. The class of unitary strongly prime rings is a special class of rings and the corresponding radical is called the unitary strongly prime radical. In this paper we prove some results on unitary strongly prime rings. The results are applied to study the unitary strongly prime radical of...
متن کاملPrime Radicals of Skew Laurent Polynomial Rings
Let R be a ring with an automorphism σ. An ideal I of R is σ-ideal of R if σ(I) = I. A proper ideal P of R is σ-prime ideal of R if P is a σ-ideal of R and for σ-ideals I and J of R, IJ ⊆ P implies that I ⊆ P or J ⊆ P . A proper ideal Q of R is σ-semiprime ideal of Q if Q is a σ-ideal and for a σ-ideal I of R, I2 ⊆ Q implies that I ⊆ Q. The σ-prime radical is defined by the intersection of all ...
متن کاملOn the Prime Model Property
Assume T is superstable, Φ(x) is a formula over ∅, Q = Φ(M∗) is countable and KQ = {M : M is countable and Φ(M) = Q}. We investigate models in KQ assuming KQ has the prime model property. We prove some corollaries on the number of models inKQ. We show an example of an ω-stable T and Q with KQ having exactly 3 models. First we fix the general set-up. Throughout, T is a countable complete theory ...
متن کاملProperties of Armendariz Rings and Weak Armendariz Rings
We consider some properties of Armendariz and rigid rings. We prove that the direct product of rigid (weak rigid), weak Armendariz rings is a rigid (weak rigid), weak Armendariz ring. On the assumption that the factor ring R/I is weak Armendariz, where I is nilpotent ideal, we prove that R is a weak Armendariz ring. We also prove that every ring isomorphism preserves weak skew Armendariz struct...
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ژورنال
عنوان ژورنال: Journal of the Korean Mathematical Society
سال: 2013
ISSN: 0304-9914
DOI: 10.4134/jkms.2013.50.5.973