EuDML | Browse

All rings considered are commutative with unit. A ring R is SISI (in Vámos' terminology) if every subdirectly irreducible factor ring R/I is self-injective. SISI rings include Noetherian rings, Morita rings and almost maximal valuation rings ([V1]). In [F3] we raised the question of whether a polynomial ring R[x] over a SISI ring R is again SISI. In this paper we show this is not the case.

Polynomial rings with coefficients in an intersection of fibred products. (Anneaux de polynômes à coefficients dans une intersection de produits fibrés.)

Ayache, A. (1999)

Portugaliae Mathematica

Polynomials with values which are powers of integers

Rachid Boumahdi, Jesse Larone (2018)

Archivum Mathematicum

Let $P$ be a polynomial with integral coefficients. Shapiro showed that if the values of $P$ at infinitely many blocks of consecutive integers are of the form $Q (m)$ , where $Q$ is a polynomial with integral coefficients, then $P (x) = Q (R (x))$ for some polynomial $R$ . In this paper, we show that if the values of $P$ at finitely many blocks of consecutive integers, each greater than a provided bound, are of the form $m^{q}$ where $q$ is an integer greater than 1, then $P (x) = {(R (x))}^{q}$ for some polynomial $R (x)$ .

P-orderings and polynomial functions on arbitrary subsets of Dedekind rings.

Manjul Bhargava (1997)

Journal für die reine und angewandte Mathematik

Porjective Modules over Polynomial Rings.

Daniel Quillen (1976)

Inventiones mathematicae

Preservation of the properties of the polynomial ring of the power series ring in the class of finite conductor rings.

González, Nelsy, Sepúlveda, Omaida, Lezama, Oswaldo (2004)

Boletín de la Asociación Matemática Venezolana

Pretty cleanness and filter-regular sequences

Somayeh Bandari, Kamran Divaani-Aazar, Ali Soleyman Jahan (2014)

Czechoslovak Mathematical Journal

Let $K$ be a field and $S = K [x_{1}, ..., x_{n}]$ . Let $I$ be a monomial ideal of $S$ and $u_{1}, ..., u_{r}$ be monomials in $S$ . We prove that if $u_{1}, ..., u_{r}$ form a filter-regular sequence on $S / I$ , then $S / I$ is pretty clean if and only if $S / (I, u_{1}, ..., u_{r})$ is pretty clean. Also, we show that if $u_{1}, ..., u_{r}$ form a filter-regular sequence on $S / I$ , then Stanley’s conjecture is true for $S / I$ if and only if it is true for $S / (I, u_{1}, ..., u_{r})$ . Finally, we prove that if $u_{1}, ..., u_{r}$ is a minimal set of generators for $I$ which form either a $d$ -sequence, proper sequence or strong $s$ -sequence (with respect to the reverse lexicographic...

Currently displaying 221 – 240 of 333

Previous Page 12 Next

Displaying 221 – 240 of 333

Polynomes à valeurs entières sur un anneau non analytiquement irréductible.

Polynômes de Barsky

Polynomial Cycles in Finitely Generated Domains.

Polynomial Extensions and Excision for K1 .

Polynomial fibre rings of algebras over noetherian rings.

Polynomial Ring in Two Variables Over a D.V.R.: A Criterion.

Polynomial rings over Jacobson-Hilbert rings.

Polynomial rings with coefficients in an intersection of fibred products. (Anneaux de polynômes à coefficients dans une intersection de produits fibrés.)

Polynomials with values which are powers of integers

P-orderings and polynomial functions on arbitrary subsets of Dedekind rings.

Porjective Modules over Polynomial Rings.

Preservation of the properties of the polynomial ring of the power series ring in the class of finite conductor rings.

Pretty cleanness and filter-regular sequences

Primary decomposition of torsion $R [X]$ -modules.

Primary ideals with finitely generated radical in a commutative ring.

Product formulas for resultants and Chow forms.

Projective modules and approximation couples

Projective modules over real affine algebras.

Projektive Moduln über Polynomringen A[t1,...,Tm] mit einem regulären Grundring A.

Quadratic forms associated with projective modules over quaternion algebras.

Currently displaying 221 – 240 of 333