A generalization of a theorem of Faith and Menal and applications.
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Tsuda, Kentaro (2000)
International Journal of Mathematics and Mathematical Sciences
M. Petrich, V. Gould (1990)
Semigroup forum
Bhat, Vijay Kumar (2006)
Lobachevskii Journal of Mathematics
Hashemi, Ebrahim (2008)
The New York Journal of Mathematics [electronic only]
Lomp, Christian, Peña P., Alirio J. (2000)
Divulgaciones Matemáticas
Philippe Loustaunau (1990)
Fundamenta Mathematicae
Kenneth S. Brown, R. Geoghegan (1984)
Inventiones mathematicae
M. Tamer Koşan, Tsiu-Kwen Lee, Yiqiang Zhou (2013)
Colloquium Mathematicae
Let R[x] and R[[x]] respectively denote the ring of polynomials and the ring of power series in one indeterminate x over a ring R. For an ideal I of R, denote by [R;I][x] the following subring of R[[x]]: [R;I][x]: = : ∃ 0 ≤ n∈ ℤ such that , ∀ i ≥ n. The polynomial and power series rings over R are extreme cases where I = 0 or R, but there are ideals I such that neither R[x] nor R[[x]] is isomorphic to [R;I][x]. The results characterizing polynomial rings or power series rings with a certain ring...
Kenneth G. Wolfson (1989)
Mathematische Zeitschrift
Patrick. F. Smith, Dinh Van Huynh (1990)
Banach Center Publications
John Dauns (1991)
Forum mathematicum
Poole, David G., Stewart, Patrick N. (1995)
International Journal of Mathematics and Mathematical Sciences
L. Lawson (1971)
Semigroup forum
M. Artin (1987)
Inventiones mathematicae
Kamal, Mahmoud A., Menshawy, Amany M. (2003)
International Journal of Mathematics and Mathematical Sciences
Rainer Schulz (1983)
Manuscripta mathematica
Mario Petrich, Ursula Müller (1971)
Journal für die reine und angewandte Mathematik
Malliavin, Marie-Paule (1983/1984)
Portugaliae mathematica
Jorge Martinez, Eric R. Zenk (2005)
Commentationes Mathematicae Universitatis Carolinae
This paper continues the investigation into Krull-style dimensions in algebraic frames. Let be an algebraic frame. is the supremum of the lengths of sequences of (proper) prime elements of . Recently, Th. Coquand, H. Lombardi and M.-F. Roy have formulated a characterization which describes the dimension of in terms of the dimensions of certain boundary quotients of . This paper gives a purely frame-theoretic proof of this result, at once generalizing it to frames which are not necessarily...
P. N. Anh (1986)
Rendiconti del Seminario Matematico della Università di Padova
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