Abdolghafoor ALLAHYARİ, Mohammad Hossein HOSSEİNİ

Holder valuation and holder rigidity for right ring of fractions

ISSN: 2147-5520
Başlangıç: 2015
Yayıncı: Biska Bilişim

The purpose of this article is to introduce the notion of (C1,C2)-Holder Krull valuation on right ring of fractions ( with respect to right denominator set S in a ring R). It is proved that if R is a ring satisfying in Holder rigidity condition, and S a right permutable set of regular elements in R, then the right ring of fractions R′= Q Â(R) with respect to S satisfies in H¨older rigidity condition. This results provide an extension of the Garsia theorem (see [2]) for right ring of fractions.

Keywords:

Valuation Holder valuation, Holder equivalent,

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O. Endler, Valuation Theory, New York, Springer-Verlag, (1972).
E. Munoz Garcia, Holder absolute values are equivalent to classicalones, Proc. Amer. Math. Soc, 127(7), 1967-1971, (1999).
J. A. Huckaba, Commutative Rings with Zero Divisors, New York, Marcel Dekker, Inc (1988).
M. Knebusch, D. Zhang, Manis Valuations and Prufer Extensions, I. A new chapter in commutative algebra. Lecture Notes in Math. 1791. Berlin, Springer-Verlage, (2002).
T. Y. Lam, A First Course in Noncommutative Rings, Springer-Verlag, (1991).
M. Manis, Valuations on a commutative ring, Proc. Amer. Math. Soc, 20, 193-198, (1969).
P. Ribenboim, The theorie des Valuations, Montreal, Less presses de I Universite de Montreal (1964).
O. F. G. Schilling, The theory of Valuations, New York, Amer. Math. Soc, Thomas, J. J, (1978). Set theory, New York, Academic press, Inc (1952).