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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.
@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 -