Sums and products of intervals in ordered semigroups
We show a simple example for ordered semigroup 𝕊 = 𝕊 (+,⩽) that 𝕊 ⊆ℝ (ℝ denotes the real line) and ]a, b[ + ]c, d[ = ]a + c, b + d[ for all a, b, c, d ∈ 𝕊 such that a < b and c < d, but the intervals are no translation invariant, that is, the equation c +]a, b[ = ]c + a, c + b[ is not always f...
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| Format: | Article |
| Language: | English |
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Sciendo
2021-06-01
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| Series: | Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica |
| Subjects: | |
| Online Access: | https://doi.org/10.2478/auom-2021-0025 |
| _version_ | 1811272286225825792 |
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| author | Glavosits T. Karácsony Zs. |
| author_facet | Glavosits T. Karácsony Zs. |
| author_sort | Glavosits T. |
| collection | DOAJ |
| description | We show a simple example for ordered semigroup 𝕊 = 𝕊 (+,⩽) that 𝕊 ⊆ℝ (ℝ denotes the real line) and ]a, b[ + ]c, d[ = ]a + c, b + d[ for all a, b, c, d ∈ 𝕊 such that a < b and c < d, but the intervals are no translation invariant, that is, the equation c +]a, b[ = ]c + a, c + b[ is not always fulfilled for all elements a, b, c ∈ 𝕊 such that a < b. |
| first_indexed | 2024-04-12T22:37:39Z |
| format | Article |
| id | doaj.art-b5f17161981c427c86e851af5d9b6186 |
| institution | Directory Open Access Journal |
| issn | 1844-0835 |
| language | English |
| last_indexed | 2024-04-12T22:37:39Z |
| publishDate | 2021-06-01 |
| publisher | Sciendo |
| record_format | Article |
| series | Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica |
| spelling | doaj.art-b5f17161981c427c86e851af5d9b61862022-12-22T03:13:50ZengSciendoAnalele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica1844-08352021-06-0129218719810.2478/auom-2021-0025Sums and products of intervals in ordered semigroupsGlavosits T.0Karácsony Zs.1Department of Applied Mathematics, University of Miskolc, Miskolc-Egyetemvaros, Hungary, H-3515.Department of Applied Mathematics, University of Miskolc, Miskolc-Egyetemvaros, Hungary, H-3515.We show a simple example for ordered semigroup 𝕊 = 𝕊 (+,⩽) that 𝕊 ⊆ℝ (ℝ denotes the real line) and ]a, b[ + ]c, d[ = ]a + c, b + d[ for all a, b, c, d ∈ 𝕊 such that a < b and c < d, but the intervals are no translation invariant, that is, the equation c +]a, b[ = ]c + a, c + b[ is not always fulfilled for all elements a, b, c ∈ 𝕊 such that a < b.https://doi.org/10.2478/auom-2021-0025intervalordered dense abelian groupordered fieldprimary 39b22 |
| spellingShingle | Glavosits T. Karácsony Zs. Sums and products of intervals in ordered semigroups Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica interval ordered dense abelian group ordered field primary 39b22 |
| title | Sums and products of intervals in ordered semigroups |
| title_full | Sums and products of intervals in ordered semigroups |
| title_fullStr | Sums and products of intervals in ordered semigroups |
| title_full_unstemmed | Sums and products of intervals in ordered semigroups |
| title_short | Sums and products of intervals in ordered semigroups |
| title_sort | sums and products of intervals in ordered semigroups |
| topic | interval ordered dense abelian group ordered field primary 39b22 |
| url | https://doi.org/10.2478/auom-2021-0025 |
| work_keys_str_mv | AT glavositst sumsandproductsofintervalsinorderedsemigroups AT karacsonyzs sumsandproductsofintervalsinorderedsemigroups |