Coregularity of order-preserving self-mapping semigroups of fences
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A fence is an ordered set that the order forms a path with alternating orientation. Let \(\bf F=\fen\) be a fence and let \(OT(\bf F)\) be the semigroup of all order-preserving self-mappings of \(\bf F\). We prove that \(OT(\bf F)\) is coregular if and only if \(|F|\leq 2\). We characterize all coregular elements in \(OT(\bf F)\) when \(\bf F\) is finite. For any subfence \(\bf S\) of \(\bf F\), we show that the set \(COT_S(\bf F)\) of all order-preserving self-mappings in \(OT(\bf F)\) having \(S\) as their range forms a coregular subsemigroup of \(OT(\bf F)\). Under some conditions, we show that a union of \(COT_S(\bf F)\)'s forms a coregular subsemigroup of \(OT(\bf F)\).
Abstract
A fence is an ordered set that the order forms a path with alternating orientation. Let \(\bf F=\fen\) be a fence and let \(OT(\bf F)\) be the semigroup of all order-preserving self-mappings of \(\bf F\). We prove that \(OT(\bf F)\) is coregular if and only if \(|F|\leq 2\). We characterize all coregular elements in \(OT(\bf F)\) when \(\bf F\) is finite. For any subfence \(\bf S\) of \(\bf F\), we show that the set \(COT_S(\bf F)\) of all order-preserving self-mappings in \(OT(\bf F)\) having \(S\) as their range forms a coregular subsemigroup of \(OT(\bf F)\). Under some conditions, we show that a union of \(COT_S(\bf F)\)'s forms a coregular subsemigroup of \(OT(\bf F)\).
참고문헌 (16)
- G. Bijev, "Coregular semigroups, Notes on Semigroups VI", pp.1~11 (1980)
- F. A. Cezus, "Maximal ideals of semigroups of endo-morphsims", Bull. Aust. Math. Soc, 12, pp.211~225 (1975)
- J. Chvalina, "Coregularity of endomorphism monoids of unars", Arch. Math, 20(1), pp.43~48 (1984)
- J. Demetrovics, "Algebraic properties of crowns and fences", Order, 6(1), pp.91~99 (1989)
- I. Dimitrova, "Coregular semigroups of full transformations", Demonstr. Math, 44(4), pp.739~753 (2011)
- J. D. Farley, "The number of order-preserving maps between fences and crowns", Order, 12(1), pp.5~44 (1995)
- L. M. Gluskin, "Isotone transformation semigroups", Uspekhi Mat. Nauk, 16(5), pp.157~162 (1961)
- P. M. Higgins, "Generating the full transformation semi-groups using order-preserving mappings", Glasg. Math. J, 45(3), pp.557~566 (2003)
- V. I. Kim, "Regularity conditions for semigroups of isotone trans-formations of countable chains", J. Math. Sci, 152(2), pp.203~208 (2008)
- E. S. Lyapin, "An abstract characteristic of a class of endomorphism semigroup of sys-tems of general view", Mat. Sb, 70(2), pp.173~179 (1966)
- M. Ma, "Regularity and Green’s relation for finite E-order-preserving transformations semigroups", Semigroup Forum, 80(1), pp.164~173 (2010)
- K. D. Magill, Jr., "Green’s relations for regular elements of semigroups of endomorphisms", Canad. J. Math, 26(6), pp.1484~1497 (1974)
- I. V. Pozdnyakova, "Semigroups of endomorphisms of some infinite monounary algebras", J. Math. Sci, 190(5), pp.658~668 (2013)
- S. Radeleczki, "The automorphism group of unary algebras", Math. Pannon, 7(2), pp.253~271 (1996)
- A. Rutkowski, "The formula for the number of order-preserving self-mappings of a fence", Order, 9(2), pp.127~137 (1992)
- Ping Zhao, "REGULARITY AND GREEN'S RELATIONS ON SEMIGROUPS OF TRANSFORMATION PRESERVING ORDER AND COMPRESSION", 대한수학회보, 49(5), pp.1015~1025 (2012), 대한수학회