Geodesic
ON THE WEAK GROTHENDIECK GROUP OF A BEZOUT RING
Glasgow mathematical journal, Tome 58 (2016) no. 3, pp. 617-635

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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 K 0(R) obtains the alternative description. 
SOROKIN, O. S. ON THE WEAK GROTHENDIECK GROUP OF A BEZOUT RING. Glasgow mathematical journal, Tome 58 (2016) no. 3, pp. 617-635. doi: 10.1017/S0017089515000373
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     title = {ON {THE} {WEAK} {GROTHENDIECK} {GROUP} {OF} {A} {BEZOUT} {RING}},
     journal = {Glasgow mathematical journal},
     pages = {617--635},
     year = {2016},
     volume = {58},
     number = {3},
     doi = {10.1017/S0017089515000373},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089515000373/}
}
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