Prime Elements and Prime Sequences in Polynomial Rings
نویسندگان
چکیده
منابع مشابه
Prime Polynomial Sequences
Let F(x) be a polynomial with integral coefficients of degree d >_ 2 such that F(n) >_ 1 for all it 3 1 . Let OF = {F(n)Í„ , . Then F(tr) is called prime in OF if F(u) is not the product of strictly smaller terms of &F . It is proved that if F(x) is not of the form a(bx+c)d, then almost all terms of (! r are prime in O F. Let 0 = be a sequence of positive integers . Then a,, E & is called compo...
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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 کاملAssociated Prime Ideals of Skew Polynomial Rings
In this paper, it has been proved that for a Noetherian ring R and an automorphism σ of R, an associated prime ideal of R[x, σ] or R[x, x−1, σ] is the extension of its contraction to R and this contraction is the intersection of the orbit under σ of some associated prime ideal of R. The same statement is true for minimal prime ideals also. It has also been proved that for a Noetherian Q-algebra...
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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 ...
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In this paper we investigate the sufficiency criteria which guarantee the classical localization of a bounded ring at its prime ideals.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1978
ISSN: 0002-9939
DOI: 10.2307/2042527