Skip to content
Back to outputs

Value semigroups, value quantales, and positivity domains

Research output: Contribution to journalArticlepeer-review

Standard

Value semigroups, value quantales, and positivity domains. / Weiss, Ittay.

In: Journal of Pure and Applied Algebra, Vol. 223, No. 2, 01.02.2019, p. 844-866.

Research output: Contribution to journalArticlepeer-review

Harvard

Weiss, I 2019, 'Value semigroups, value quantales, and positivity domains', Journal of Pure and Applied Algebra, vol. 223, no. 2, pp. 844-866. https://doi.org/10.1016/j.jpaa.2018.05.002

APA

Vancouver

Author

Weiss, Ittay. / Value semigroups, value quantales, and positivity domains. In: Journal of Pure and Applied Algebra. 2019 ; Vol. 223, No. 2. pp. 844-866.

Bibtex

@article{cc633f534ccd463cbec7171a09942905,
title = "Value semigroups, value quantales, and positivity domains",
abstract = "In 1981 and 1997 Kopperman and Flagg, respectively, proved that every topological space is metrisable, provided the symmetry and separation axioms are removed from the requirements on the metric, and the metric is allowed to take values in, respectively, a value semigroup or a value quantale. Seeking to construct a value quantale from a value semigroup we focus on a small portion of the structure present in a value semigroup, comprising what we call a positivity domain, and we construct its enveloping value quantale, forming part of a detailed comparison between value semigroups and value quantales. We obtain a representation theorem for value quantales in terms of positivity domains, and we outline how products of positivity domains can be used in the theory of continuity spaces instead of (the non-existent) products of value quantales.",
keywords = "value quantale, value semigroup, continuity space, ordered semigroup, ordered monoid",
author = "Ittay Weiss",
note = "12 months embargo",
year = "2019",
month = feb,
day = "1",
doi = "10.1016/j.jpaa.2018.05.002",
language = "English",
volume = "223",
pages = "844--866",
journal = "Journal of Pure and Applied Algebra",
issn = "0022-4049",
publisher = "Elsevier",
number = "2",

}

RIS

TY - JOUR

T1 - Value semigroups, value quantales, and positivity domains

AU - Weiss, Ittay

N1 - 12 months embargo

PY - 2019/2/1

Y1 - 2019/2/1

N2 - In 1981 and 1997 Kopperman and Flagg, respectively, proved that every topological space is metrisable, provided the symmetry and separation axioms are removed from the requirements on the metric, and the metric is allowed to take values in, respectively, a value semigroup or a value quantale. Seeking to construct a value quantale from a value semigroup we focus on a small portion of the structure present in a value semigroup, comprising what we call a positivity domain, and we construct its enveloping value quantale, forming part of a detailed comparison between value semigroups and value quantales. We obtain a representation theorem for value quantales in terms of positivity domains, and we outline how products of positivity domains can be used in the theory of continuity spaces instead of (the non-existent) products of value quantales.

AB - In 1981 and 1997 Kopperman and Flagg, respectively, proved that every topological space is metrisable, provided the symmetry and separation axioms are removed from the requirements on the metric, and the metric is allowed to take values in, respectively, a value semigroup or a value quantale. Seeking to construct a value quantale from a value semigroup we focus on a small portion of the structure present in a value semigroup, comprising what we call a positivity domain, and we construct its enveloping value quantale, forming part of a detailed comparison between value semigroups and value quantales. We obtain a representation theorem for value quantales in terms of positivity domains, and we outline how products of positivity domains can be used in the theory of continuity spaces instead of (the non-existent) products of value quantales.

KW - value quantale

KW - value semigroup

KW - continuity space

KW - ordered semigroup

KW - ordered monoid

U2 - 10.1016/j.jpaa.2018.05.002

DO - 10.1016/j.jpaa.2018.05.002

M3 - Article

VL - 223

SP - 844

EP - 866

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

SN - 0022-4049

IS - 2

ER -

ID: 9470393