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

Voir la notice de l'article provenant de la source Cambridge University Press

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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[1] 1. Bass, H., K-theory and stable algebra, Publ. Math. 22 (1964), 5–60. Google Scholar

[2] 2. Bourbaki, N., Algèbre, Ch. X (Masson, Paris, 1980). Google Scholar

[3] 3. Bourbaki, N., Elements de mathematique. Fase. XXVII. Algebre commutative. Chap. 1: Modules plats (Hermann, Paris, 1961). Google Scholar

[4] 4. Guralnick, R. M., Matrix equivalence and isomorphism of modules, Linear Algebra Appl. 43 (1982), 125–136. Google Scholar | DOI

[5] 5. Goodearl, K. R., Von Neumann regular rings (Pitman, London, 1979), 369. Google Scholar

[6] 6. Goodearl, K. R., Torsion in K of unit-regular rings, Proc. Edinburgh Math. Soc. 38 (1995), 331–341. Google Scholar | DOI

[7] 7. Henriksen, M., On a class of regular rings that are elementary divisor rings, Arch. Math. (Basel) 24 (1973), 133–141. Google Scholar

[8] 8. Kaplansky, I., Elementary divisors and modules, Trans. Amer. Math. Soc. 66 (1949), 464–491. Google Scholar

[9] 9. Lambek, J., Lectures on rings and modules (Blaisdell Publishing, 1966). Google Scholar

[10] 10. Larsen, M., Levis, W. and Shores, T., Elementary divisor rings and finitely presented modules, Trans. Amer. Math. Soc. 187 (1974), 231–248. Google Scholar

[11] 11. Milnor, J. W., Introduction to algebraic K-theory, Ann. Math. Stud. 72 (1971), 184. Google Scholar

[12] 12. Nicholson, W. K. and Sanchez, E., Campos Rings with the dual of the isomorphism theorem, J. Algebra 271 (2004), 391–406. Google Scholar

[13] 13. Shores, T., Modules over semihereditary Bezout rings, Proc. Amer. Math. Soc. 46 (2) (1974), 211–213. Google Scholar | DOI

[14] 14. Shores, T., Decomposition of modules and matrices, Bull. Amer. Math. Soc. 79 (6) (1973), 1277–1280. Google Scholar

[15] 15. Vasserstein, L. N., The stable rank of rings and dimensionality of topological spaces, Functional Anal. Appl. 5 (1971), 102–110. Google Scholar | DOI

[16] 16. Warfield, R. B., Exchange rings and decompositions of modules, Math. Ann. 199 (1972), 31–36. Google Scholar

[17] 17. Weibel, C. A., The K-book: An introduction to algebraic K-theory, Grad. Stud. Math. 145 (2013), 618. Google Scholar | DOI

[18] 18. Zabavsky, B. V., Diagonal reduction of matrices over rings, Mathematical Studies, Monograph Series, vol. XVI (VNTL Publishers, 2012), 251. Google Scholar

[19] 19. Zabavsky, B. V., Diagonal reduction of matrices over finite stable range rings, Math. Stud. 41 (1) (2014), 101–108. Google Scholar

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