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A domain R is called a maximal "non-S" subring of a field L if R ⊂ L, R is not an S-domain and each domain T such that R ⊂ T ⊆ L is an S-domain. We show that maximal "non-S" subrings R of a field L are the integrally closed pseudo-valuation domains satisfying dim(R) = 1, dimv(R) = 2 and L = qf(R).
Jarboui, Noômen. "When is each proper overring of R an S(Eidenberg)-domain?." Publicacions Matemàtiques 46.2 (2002): 435-440. <http://eudml.org/doc/41456>.
@article{Jarboui2002, abstract = {A domain R is called a maximal "non-S" subring of a field L if R ⊂ L, R is not an S-domain and each domain T such that R ⊂ T ⊆ L is an S-domain. We show that maximal "non-S" subrings R of a field L are the integrally closed pseudo-valuation domains satisfying dim(R) = 1, dimv(R) = 2 and L = qf(R).}, author = {Jarboui, Noômen}, journal = {Publicacions Matemàtiques}, keywords = {Anillos conmutativos; Extensión; Dimensión de Krull; -domain; pseudo-valuation domains; Seidenberg domain}, language = {eng}, number = {2}, pages = {435-440}, title = {When is each proper overring of R an S(Eidenberg)-domain?}, url = {http://eudml.org/doc/41456}, volume = {46}, year = {2002}, }
TY - JOUR AU - Jarboui, Noômen TI - When is each proper overring of R an S(Eidenberg)-domain? JO - Publicacions Matemàtiques PY - 2002 VL - 46 IS - 2 SP - 435 EP - 440 AB - A domain R is called a maximal "non-S" subring of a field L if R ⊂ L, R is not an S-domain and each domain T such that R ⊂ T ⊆ L is an S-domain. We show that maximal "non-S" subrings R of a field L are the integrally closed pseudo-valuation domains satisfying dim(R) = 1, dimv(R) = 2 and L = qf(R). LA - eng KW - Anillos conmutativos; Extensión; Dimensión de Krull; -domain; pseudo-valuation domains; Seidenberg domain UR - http://eudml.org/doc/41456 ER -