The R-height of semigroups and their bi-ideals

2022/04/07 by Miller, Craig
#20M10 #20M12 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2204.03377

Abstract

The R-height of a semigroup S is the height of the poset of R-classes of S, i.e. the supremum of the lengths of chains of R-classes. Given a semigroup S with finite R-height, we establish bounds on the R-height of bi-ideals, one-sided ideals and two-sided ideals; in particular, these substructures inherit the property of having finite R-height. We then investigate whether these bounds can be attained.

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