Mathematics and Statistics Vol. 3(1), pp. 16 - 24
DOI: 10.13189/ms.2015.030104
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On the Weak Grothendieck Group of a Morphic Ring and its Representations

Sorokin O.S. ^*
Department of Algebra and Logic, Faculty of Mechanics and Mathematics, Ivan Franko National University of Lviv, 79059, Lviv, Ukraine

ABSTRACT

The K-theoretical aspect of the commutative mophic rings is established using the arithmetical properties of the morphic rings in order to obtain a ring of all Smith normal forms of matrices over the morphic ring. The internal structure and basic properties of such rings are discussed as well as their presentations by the Witt vectors. In a case of a commutative von Neumann regular rings the famous Grothendieck group K₀(R) obtains the alternative description.

KEYWORDS
Grothendieck Group, Morphic Ring, K-theory, Witt Ring, von Neumann Regular Ring, Smith Normal Form, Bezout Ring, Principal Ideals

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Sorokin O.S. , "On the Weak Grothendieck Group of a Morphic Ring and its Representations," Mathematics and Statistics, Vol. 3, No. 1, pp. 16 - 24, 2015. DOI: 10.13189/ms.2015.030104.

(b). APA Format:
Sorokin O.S. (2015). On the Weak Grothendieck Group of a Morphic Ring and its Representations. Mathematics and Statistics, 3(1), 16 - 24. DOI: 10.13189/ms.2015.030104.