Abstract

GRANADOS PINZON, C.  and  OLAYA LEON, W.. Total rings of fractions and Hermite rings. Ciencia en Desarrollo [online]. 2020, vol.11, n.2, pp.125-134.  Epub Mar 23, 2021. ISSN 0121-7488.  https://doi.org/10.19053/01217488.v11.n2.2020.10223.

In this paper, we show general properties of total rings of fractions and of Hermite rings. We study the relationships between those rings and the finite dimensional K-algebras. A finite dimensional K-algebra is a commutative algebra with unit such that this is finite dimensional as vector space over a field K. We proof that the finite dimensional K-algebras are total rings of fractions and also Hermite rings. In addition, we show that direct product of fields is another example of total ring of fractions and Hermite ring.

Keywords : Localization; direct product of rings; Hermite ring and finite dimensional K-algebra.

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