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ON THE WEAK GROTHENDIECK GROUP OF A BEZOUT RING

Part of: Arithmetic rings and other special rings Grothendieck groups and $K_0$ Commutative algebra: Homological methods

Published online by Cambridge University Press:  21 July 2015

O. S. SOROKIN
O. S. SOROKIN*
Affiliation:
Department of Algebra and Logic, Faculty of Mechanics and Mathematics, Ivan Franko National University of L'viv, 1 Universytetska str., 79000, Lviv, Ukraine e-mail: neverhalluet@gmail.com
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Abstract

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The K-theoretical aspect of the commutative Bezout rings is established using the arithmetical properties of the Bezout rings in order to obtain a ring of all Smith normal forms of matrices over the Bezout 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.

MSC classification

Primary: 19A49: $K_0$ of other rings
Secondary: 13D15: Grothendieck groups, $K$-theory 13F35: Witt vectors and related rings
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 58 , Issue 3 , September 2016 , pp. 617 - 635
Copyright
Copyright © Glasgow Mathematical Journal Trust 2015 

References

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