Thomas S. Shores
Abstract
It is shown that every commutative semihereditary Bezout ring of Krull dimension at most one is an elementary divisor ring. A consequence is that the ring of polynomials in one indeterminate over a von Neumann regular ring is an elementary divisor ring.
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It is shown that every commutative semihereditary Bezout ring of Krull dimension at most one is an elementary divisor ring. A consequence is that the ring of polynomials in one indeterminate over a von Neumann regular ring is an elementary divisor ring.
Key concepts: Krull dimension, Mathematics, Von Neumann regular ring, Commutative ring, Ring (chemistry), Divisor (algebraic geometry), Pure mathematics, Principal ideal ring