Polynomial rings over Jacobson-Hilbert rings.

Faith, Carl. "Polynomial rings over Jacobson-Hilbert rings.." Publicacions Matemàtiques 33.1 (1989): 85-97. <http://eudml.org/doc/41069>.

@article{Faith1989,
abstract = {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.},
author = {Faith, Carl},
journal = {Publicacions Matemàtiques},
keywords = {Anillos conmutativos; Anillos de polinomios; Anillos de Morita; Anillos de Von Neumann; Ideal maximal; Monica rings; SISI; self-injective; Jacobson-Hilbert rings; Morita rings; von Neumann rings},
language = {eng},
number = {1},
pages = {85-97},
title = {Polynomial rings over Jacobson-Hilbert rings.},
url = {http://eudml.org/doc/41069},
volume = {33},
year = {1989},
}

TY - JOUR
AU - Faith, Carl
TI - Polynomial rings over Jacobson-Hilbert rings.
JO - Publicacions Matemàtiques
PY - 1989
VL - 33
IS - 1
SP - 85
EP - 97
AB - 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.
LA - eng
KW - Anillos conmutativos; Anillos de polinomios; Anillos de Morita; Anillos de Von Neumann; Ideal maximal; Monica rings; SISI; self-injective; Jacobson-Hilbert rings; Morita rings; von Neumann rings
UR - http://eudml.org/doc/41069
ER -