Stability of characters and filters for weighted semilattices

Yemon Choi; Mahya Ghandehari; Hung Le Pham

doi:10.1007/s00233-020-10147-w

Stability of characters and filters for weighted semilattices

Yemon Choi
, Mahya Ghandehari
, Hung Le Pham

University of Delaware
Victoria University of Wellington

Research output: Contribution to Journal/Magazine › Journal article › peer-review

1 Citation (Scopus)

42 Downloads (Pure)

Abstract

We continue the study of the AMNM property for weighted semilattices that was initiated in [Y. Choi, J. Austral. Math. Soc. 95 (2013), no. 1, 36-67; arXiv 1203.6691 ] . We reformulate this in terms of stability of filters with respect to a given weight function, and then provide a combinatorial condition which is necessary and sufficient for this "filter stability" property to hold. Examples are given to show that this new condition allows for easier and unified proofs of some results in [Choi, ibid. ] , and furthermore allows us to verify the AMNM property in situations not covered by the results of that paper. As a final application, we show that for a large class of semilattices, arising naturally as union-closed set systems, one can always construct weights for which the AMNM property fails.

Original language	English
Pages (from-to)	86-103
Number of pages	18
Journal	Semigroup Forum
Volume	102
Issue number	1
Early online date	24/12/2020
DOIs	https://doi.org/10.1007/s00233-020-10147-w
Publication status	Published - 11/02/2021

Access to Document

10.1007/s00233-020-10147-wLicence: CC BY

cgp_arx1901_00082v3Accepted author manuscript, 209 KBLicence: CC BY: Creative Commons Attribution 4.0 International License

https://arxiv.org/abs/1901.00082v3Licence: CC BY-NC: Creative Commons Attribution-NonCommercial 4.0 International License
https://link.springer.com/article/10.1007/s00233-020-10147-wLicence: CC BY: Creative Commons Attribution 4.0 International License

London Mathematical Society - Visitor Grant (Scheme 2)
Choi, Y. (Principal Investigator)
London Mathematical Society
1/10/14 → 28/10/14
Project: Research

Approximate homomorphisms: some old and new results
Choi, Y. (Keynote speaker)
11/07/2019 → 18/07/2019
Activity: Talk or presentation types › Invited talk

Cite this

@article{54dd293cfcf94285883aeac44771b4ce,

title = "Stability of characters and filters for weighted semilattices",

abstract = "We continue the study of the AMNM property for weighted semilattices that was initiated in [Y. Choi, J. Austral. Math. Soc. 95 (2013), no. 1, 36-67; arXiv 1203.6691 ] . We reformulate this in terms of stability of filters with respect to a given weight function, and then provide a combinatorial condition which is necessary and sufficient for this {"}filter stability{"} property to hold. Examples are given to show that this new condition allows for easier and unified proofs of some results in [Choi, ibid. ] , and furthermore allows us to verify the AMNM property in situations not covered by the results of that paper. As a final application, we show that for a large class of semilattices, arising naturally as union-closed set systems, one can always construct weights for which the AMNM property fails.",

author = "Yemon Choi and Mahya Ghandehari and Pham, \{Hung Le\}",

year = "2021",

month = feb,

day = "11",

doi = "10.1007/s00233-020-10147-w",

language = "English",

volume = "102",

pages = "86--103",

journal = "Semigroup Forum",

issn = "0037-1912",

publisher = "Springer New York",

number = "1",

}

TY - JOUR

T1 - Stability of characters and filters for weighted semilattices

AU - Choi, Yemon

AU - Ghandehari, Mahya

AU - Pham, Hung Le

PY - 2021/2/11

Y1 - 2021/2/11

N2 - We continue the study of the AMNM property for weighted semilattices that was initiated in [Y. Choi, J. Austral. Math. Soc. 95 (2013), no. 1, 36-67; arXiv 1203.6691 ] . We reformulate this in terms of stability of filters with respect to a given weight function, and then provide a combinatorial condition which is necessary and sufficient for this "filter stability" property to hold. Examples are given to show that this new condition allows for easier and unified proofs of some results in [Choi, ibid. ] , and furthermore allows us to verify the AMNM property in situations not covered by the results of that paper. As a final application, we show that for a large class of semilattices, arising naturally as union-closed set systems, one can always construct weights for which the AMNM property fails.

AB - We continue the study of the AMNM property for weighted semilattices that was initiated in [Y. Choi, J. Austral. Math. Soc. 95 (2013), no. 1, 36-67; arXiv 1203.6691 ] . We reformulate this in terms of stability of filters with respect to a given weight function, and then provide a combinatorial condition which is necessary and sufficient for this "filter stability" property to hold. Examples are given to show that this new condition allows for easier and unified proofs of some results in [Choi, ibid. ] , and furthermore allows us to verify the AMNM property in situations not covered by the results of that paper. As a final application, we show that for a large class of semilattices, arising naturally as union-closed set systems, one can always construct weights for which the AMNM property fails.

U2 - 10.1007/s00233-020-10147-w

DO - 10.1007/s00233-020-10147-w

M3 - Journal article

SN - 0037-1912

VL - 102

SP - 86

EP - 103

JO - Semigroup Forum

JF - Semigroup Forum

IS - 1

ER -

Stability of characters and filters for weighted semilattices

Abstract

Access to Document

Projects

London Mathematical Society - Visitor Grant (Scheme 2)

Activities

Approximate homomorphisms: some old and new results

Cite this