JP Journal of Algebra, Number Theory and Applications
Volume 5, Issue 3, Pages 583 - 589
(December 2005)
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EXAMPLES OF NON-COMMUTATIVE v-BEZOUT RINGS
Santi Irawati (Indonesia), Shigeru Kobayashi (Japan) and Hidetoshi Marubayashi (Japan)
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Abstract: Let V be a total valuation ring of a division ring K. It is shown that R = V[xr, s|r μ/span>Q0],the skew semigroup ring of Q0 over V, is v-Bezout which is a non-commutative version of commutative GCD-domains, where Q0 is the semigroup of nonnegative rational numbers and s is a semigroup homomorphism from Q0to Aut(V). |
Keywords and phrases: total valuation ring, v-Bezout ring. |
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