ON INTEGRALITY AND GOING-DOWN INSIDE THE FIXED RING OF A MONOID RING

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International Electronic Journal of Algebra
Volume:19 Issue:19
ON INTEGRALITY AND GOING-DOWN INSIDE THE FIXED RING OF A MONOID RING

ON INTEGRALITY AND GOING-DOWN INSIDE THE FIXED RING OF A MONOID RING

Authors : David E Dobbs, Jay Shapiro

Pages : 132-144

Doi:10.24330/ieja.266198

View : 17 | Download : 11

Publication Date : 2016-06-01

Article Type : Research Paper

Abstract :An example is given of a finitely generated abelian torsion-free monoid S on which the group G with two elements acts via semigroup automorphisms such that for any field K, when the given action is extended so that G acts on the monoid ring K[X; S] via ring automorphisms that fix K elementwise, the ring extension K[X; SG] ⊆ insert ignore into journalissuearticles values(K[X; S]);G is not integral and does not satisfy the going-down property.
Keywords : Commutative ring, ring extension, group action, fixed ring, integrality, going down, semigroup, fixed semigroup, semigroup ring, INC, LO, factor semigroup, maximal ideal, Krull dimension, orbit, locally finite

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