Height of operands over monoids satisfying the d.c.c. on orbits
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- by William R. Nico
- Proc. Amer. Math. Soc. 48 (1975), 313-320
- DOI: https://doi.org/10.1090/S0002-9939-1975-0374290-3
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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 $h(X) < sl(X)$.References
- A. H. Clifford and G. B. Preston, The algebraic theory of semigroups. Vol. II, Mathematical Surveys, No. 7, American Mathematical Society, Providence, R.I., 1967. MR 0218472
- William R. Nico, A study of operands in terms of maximal generalized orbits, J. Algebra 30 (1974), 473–484. MR 344369, DOI 10.1016/0021-8693(74)90218-X
Bibliographic Information
- © Copyright 1975 American Mathematical Society
- 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