Commutativity for a certain class of rings.
Abujabal, H.A.S., Khan, M.A. (1998)
Georgian Mathematical Journal
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Abujabal, H.A.S., Khan, M.A. (1998)
Georgian Mathematical Journal
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Abujabal, Hamza A.S. (1996)
Georgian Mathematical Journal
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Dolinka, Igor, Mudrinski, Nebojša (2004)
Novi Sad Journal of Mathematics
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Agayev, Nazim, Güngöroğlu, Gonca, Harmanci, Abdullah, Halicioğlu, S. (2011)
Bulletin of the Malaysian Mathematical Sciences Society. Second Series
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Gérard Leloup (2007)
Annales mathématiques Blaise Pascal
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Rings of formal power series with exponents in a cyclically ordered group were defined in []. Now, there exists a “valuation” on : for every in and in , we let be the first element of the support of which is greater than or equal to . Structures with such a valuation can be called cyclically valued rings. Others examples of cyclically valued rings are obtained by “twisting” the multiplication in . We prove that a cyclically valued ring is a subring of a power series...
Ismail M. Idris (2001)
Colloquium Mathematicae
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Prestel introduced a generalization of the notion of an ordering of a field, which is called a semiordering. Prestel's axioms for a semiordered field differ from the usual (Artin-Schreier) postulates in requiring only the closedness of the domain of positivity under x ↦ xa² for non-zero a, in place of requiring that positive elements have a positive product. Our aim in this work is to study this type of ordering in the case of a division ring. We show that it actually behaves just as...
Rudeanu, S. (2007)
Acta Mathematica Universitatis Comenianae. New Series
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Brešar, M., Chebotar, M.A. (2002)
Beiträge zur Algebra und Geometrie
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Crvenković, Siniša, Dolinka, Igor, Vinčić, Milovan (2002)
Beiträge zur Algebra und Geometrie
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Karim, Driss (2003)
Beiträge zur Algebra und Geometrie
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David E. Dobbs, Gabriel Picavet (2003)
Annales mathématiques Blaise Pascal
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We consider analogies between the logically independent properties of strong going-between (SGB) and going-down (GD), as well as analogies between the universalizations of these properties. Transfer results are obtained for the (universally) SGB property relative to pullbacks and Nagata ring constructions. It is shown that if are domains such that is an LFD universally going-down domain and is algebraic over , then the inclusion map satisfies GB for each . However, for any...