Filtration on a Ring Make a Quasi Valuation or Valuation Ring

Abstract

In this paper we show that if R is a filtered ring then we can define a quasi valuation ring. And there exists a valuation ring if R is some kind of filtered ring. Then we prove some properties and relations between filtered ring and quasi valuation ring and valuation ring

Keywords

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

Filtration on a ring make a quasi valuation or valuation ring

Öz

Kaynakça

1. M.H. Anjom SHoa, M. H. Hosseini, Filtered ring Derived From Valuation Ring and It’s Property, Advances in Pure Mathematics, 2014
2. 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).
3. N. S. Gopalakrishnan, Commutative algebra, oxonian press,1983.
4. 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.
5. T.Y. Lam , A First Course in Noncommutative Rings,Springer-Verlag ,1991.
6. Koji Nishida On the depth of the associated graded ring of a filtration (Journal of Algebra 285 (2005) 182–195).
7. 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).
8. David E. Rush, Rees valuations and asymptotic primes of rational powers in Noetherian rings and lattices, Journal of Algebra, 308 (2007), (295 - 320).

9. Paolo Zanardo, On _-closed Manis vluation rins,Communication in algebra, 18(3), 775-788(1990).
10. Paolo Zanardo, Construction of manis vluation rins, Communication in algebra, 21(11), 4183-4194(1993).