THE RELATION BETWEEN QUASI VALUATION AND VALUATION RING AND FILTERED RING

Abstract

In this paper we show the relation between filtered ring and quasi valuation and valuation ring . We show if is a filtered ring then we can define a quasi valuation. And if is some kind of filtered ring then we can define a valuation. Then we prove some properties and relations for

Keywords

• Filtered ring,Quasi valuation ring,Valuation ring,Strongly filtered ring

The relation between quasi valuation and valuation ring and filtered ring

Öz

Kaynakça

1. F.R. Cohen , Aaron Heap , Alexandra Pettet On the Andreadakis–Johnson filtration of the automorphism group of a free group (Journal of Algebra 329 (2011) 72–91).
2. N. S. Gopalakrishnan, Commutative algebra, oxonian press,1983.
3. Algebras, Rings and Modules by Michiel Hazewinkel CWI, Amsterdam, The Netherlands Nadiya Gubareni Technical University of Czstochowa, Poland and V.V. KirichenkoKiev Taras Shevchenko University, Kiev, Ukraine KLUWER.
4. T.Y. Lam , A First Course in Noncommutative Rings,Springer-Verlag ,1991.
5. Koji Nishida On the depth of the associated graded ring of a filtration (Journal of Algebra 285 (2005) 182–195).
6. G. Puninskia, V. Puninskayab, C. Toffalorib Decidability of the theory of modules over commutative valuation domains, Annals of Pure and Applied Logic, 145 (2007), (258 - 275).
7. David E. Rush, Rees valuations and asymptotic primes of rational powers in Noetherian rings and lattices, Journal of Algebra, 308 (2007), (295 - 320).
8. Paolo Zanardo, On _-closed Manis vluation rins,Communication in algebra, 18(3), 775-788(1990).

9. Paolo Zanardo, Construction of manis vluation rins, Communication in algebra, 21(11), 4183-4194(1993).