Filtration on a Ring Make a Quasi Valuation or Valuation Ring

Year 2014, Volume: 2 Issue: 1, 18 - 22, 01.04.2014

Mohammad Hassan Anjom Shoa

https://izlik.org/JA65GH22PJ

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

https://izlik.org/JA65GH22PJ

Abstract

References

• M.H. Anjom SHoa, M. H. Hosseini, Filtered ring Derived From Valuation Ring and It’s Property, Advances in Pure Mathematics, 2014
• 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).
• N. S. Gopalakrishnan, Commutative algebra, oxonian press,1983.
• 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.
• T.Y. Lam , A First Course in Noncommutative Rings,Springer-Verlag ,1991.
• Koji Nishida On the depth of the associated graded ring of a filtration (Journal of Algebra 285 (2005) 182–195).
• 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).
• David E. Rush, Rees valuations and asymptotic primes of rational powers in Noetherian rings and lattices, Journal of Algebra, 308 (2007), (295 - 320).
• Paolo Zanardo, On _-closed Manis vluation rins,Communication in algebra, 18(3), 775-788(1990).
• Paolo Zanardo, Construction of manis vluation rins, Communication in algebra, 21(11), 4183-4194(1993).