Real closed rings, I. Residue rings of rings of continuous functions
Gregory Cherlin, Max Dickmann (1986)
Fundamenta Mathematicae
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Gregory Cherlin, Max Dickmann (1986)
Fundamenta Mathematicae
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A. Widiger (1983)
Fundamenta Mathematicae
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O. A. S. Karamzadeh, M. Motamedi, S. M. Shahrtash (2009)
Fundamenta Mathematicae
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Ravinder Kumar, Kanchan Manaktala (1975)
Publications de l'Institut Mathématique
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Marcus Tressl (2007)
Fundamenta Mathematicae
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A super real closed ring is a commutative ring equipped with the operation of all continuous functions ℝⁿ → ℝ. Examples are rings of continuous functions and super real fields attached to z-prime ideals in the sense of Dales and Woodin. We prove that super real closed rings which are fields are an elementary class of real closed fields which carry all o-minimal expansions of the real field in a natural way. The main part of the paper develops the commutative algebra of super real closed...
O. A. S. Karamzadeh, M. Motamedi, S. M. Shahrtash (2004)
Fundamenta Mathematicae
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Right ue-rings (rings with the property of the title, i.e., with the maximality of the right socle) are investigated. It is shown that a semiprime ring R is a right ue-ring if and only if R is a regular V-ring with the socle being a maximal right ideal, and if and only if the intrinsic topology of R is non-discrete Hausdorff and dense proper right ideals are semisimple. It is proved that if R is a right self-injective right ue-ring (local right ue-ring), then R is never semiprime and...
Szeto, George, Wong, Yuen-Fat (1981)
Portugaliae mathematica
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Niels Schwartz (2010)
Annales de la faculté des sciences de Toulouse Mathématiques
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-rings are commutative rings whose factor rings modulo prime ideals are valuation rings. -rings occur most naturally in connection with partially ordered rings (= porings) and have been studied only in this context so far. The present note first develops the theory of -rings systematically, without assuming the presence of a partial order. Particular attention is paid to the question of axiomatizability (in the sense of model theory). Partially ordered -rings (-porings)...
Schutte, H.J., Wessels, S.F.G. (1973)
Portugaliae mathematica
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Ján Mináč (1982)
Mathematica Slovaca
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Gerhard O. Michler (1973)
Publications du Département de mathématiques (Lyon)
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