Valuation Theory. Part I

Grzegorz Bancerek; Hidetsune Kobayashi; Artur Korniłowicz

doi:10.2478/v10037-012-0002-4

.blurhash-client-img { display: none !important; }

Valuation Theory. Part I

Formalized Mathematics

Volume 20 (2012): Issue 1 (January 2012)

By: Grzegorz Bancerek, Hidetsune Kobayashi and Artur Korniłowicz

Open Access

|Sep 2012

Abstract

In the article we introduce a valuation function over a field [1]. Ring of non negative elements and its ideal of positive elements have been also defined.

References

Emil Artin. Algebraic Numbers and Algebraic Functions. Gordon and Breach Science Publishers, 1994.
Search in Google Scholar
Jonathan Backer, Piotr Rudnicki, and Christoph Schwarzweller. Ring ideals. Formalized Mathematics, 9(3):565-582, 2001.
Search in Google Scholar
Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.
Search in Google Scholar
Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.
Search in Google Scholar
Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.
Search in Google Scholar
Józef Białas. Properties of fields. Formalized Mathematics, 1(5):807-812, 1990.
Search in Google Scholar
Czesław Byliński. Binary operations. Formalized Mathematics, 1(1):175-180, 1990.
Search in Google Scholar
Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.
Search in Google Scholar
Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
Search in Google Scholar
Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.
Search in Google Scholar
Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.
Search in Google Scholar
Artur Korniłowicz. Quotient rings. Formalized Mathematics, 13(4):573-576, 2005.
Search in Google Scholar
Eugeniusz Kusak, Wojciech Leończuk, and Michał Muzalewski. Abelian groups, fields and vector spaces. Formalized Mathematics, 1(2):335-342, 1990.
Search in Google Scholar
Michał Muzalewski. Construction of rings and left-, right-, and bi-modules over a ring. Formalized Mathematics, 2(1):3-11, 1991.
Search in Google Scholar
Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics, 1(1):115-122, 1990.
Search in Google Scholar
Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990.
Search in Google Scholar
Wojciech A. Trybulec. Groups. Formalized Mathematics, 1(5):821-827, 1990.
Search in Google Scholar
Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990.
Search in Google Scholar
Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
Search in Google Scholar
Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.
Search in Google Scholar
Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.
Search in Google Scholar

Articles in this issue

DOI: https://doi.org/10.2478/v10037-012-0002-4 | Journal eISSN: 1898-9934 | Journal ISSN: 1426-2630

Journal RSS Feed

Language: English

Page range: 7 - 14

Published on: Sep 12, 2012

Published by: University of Białystok

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Related subjects:

Mathematics,

Logic and set theory,

Computer sciences,

Artificial intelligence

© 2012 Grzegorz Bancerek, Hidetsune Kobayashi, Artur Korniłowicz, published by University of Białystok
This work is licensed under the Creative Commons License.

Volume 20 (2012): Issue 1 (January 2012)