Diagonal reduction of matrices over commutative semihereditary Bezout rings.
Keywords:
Bezout ring, elementary divisor ring, semihereditary ring, stable range, Gelfand range 1, adequate element, Gelfand elementAbstract
All rings considered will be commutative and have identity. Recently there has been some
interest in the polynomial ring R [x], where R is a von Neumann regular ring.
References
I. Kaplansky, Elementary divisors and modules, Trans. Amer. Math. Soc. 66 (1949), 464–491.
McAdam, S., Swan, R. G., Unique comaximal factorization, J. Algebra. 276 (2004), 180–192.
Shores T., Modules over semihereditary Bezout rings, Proc. Amer. Math. Soc. 46 (1974), 211–213.
B.V. Zabavsky, Conditions for stable range of an elementary divisor rings, Comm. Algebra 45 (2017), no. 9, 4062–4066.
