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Height of operands over monoids satisfying the d.c.c. on orbits


Author: William R. Nico
Journal: Proc. Amer. Math. Soc. 48 (1975), 313-320
MSC: Primary 20M05
DOI: https://doi.org/10.1090/S0002-9939-1975-0374290-3
MathSciNet review: 0374290
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Abstract: The height, $ h(X)$, of an operand $ X$ over a monoid $ S$ satisfying the d.c.c. on orbits is defined, and is compared to the saturation length, $ sl(X)$, of $ X$. If $ h(X)$ is finite, then $ sl(X) \leq h(X)$. If $ X$ is saturated, then $ h(X)$ must be a limit ordinal. If $ h(X)$ is infinite, then it may be that $ h(X) < sl(X)$.


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DOI: https://doi.org/10.1090/S0002-9939-1975-0374290-3
Keywords: Monoid, operand, semigroup, monoid acting on a set, transformation monoid
Article copyright: © Copyright 1975 American Mathematical Society

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