Source of ?-Semigroups’ Primeness
| dc.contributor.author | Yeşil, Didem | |
| dc.contributor.author | Mekera, Rasie | |
| dc.date.accessioned | 2026-02-03T11:50:10Z | |
| dc.date.available | 2026-02-03T11:50:10Z | |
| dc.date.issued | 2025 | |
| dc.department | Çanakkale Onsekiz Mart Üniversitesi | |
| dc.description.abstract | This study aims to define the source of a ?-semigroup S’s primeness and to research some of its basic properties and the PS? subset of S as PS? = {b ? S : S?S?b = (0)}, for the ?-semigroup S with zero. Afterward, it investigates the relationships between |PS? |-reduced, |PS? |-idempotent, |PS? |-strongly idempotent, and |PS? |-regular ?-semigroup structures as follows: (i) If S is a |PS? |-idempotent ?-semigroup, then S is a |PS? |-regular ?- semigroup, (ii) If S is a |PS? |-idempotent ?-semigroup, then S is a |PS? |-reduced ?-semigroup, (iii) If S is an idempotent (regular, reduced) ?-semigroup, then S is a |PS? |-idempotent (regular, reduced) ?-semigroup, (iv) If S is a |PS? |- strongly idempotent (regular) ?-semigroup, then A is a |PA? |- strongly idempotent (regular) ?-semigroup, and (v) If S is a commutative |PS? |-regular ?-semigroup, then S is a |PS? |-reduced ?-semigroup. Moreover, this study explores the connections between the source of ?-primeness of a ?-semigroup and the aforementioned ?-semigroup structures and clarifies some theoretical parts of the study with several examples. | |
| dc.identifier.doi | 10.53570/jnt.1732995 | |
| dc.identifier.endpage | 37 | |
| dc.identifier.issn | 2149-1402 | |
| dc.identifier.issue | 52 | |
| dc.identifier.startpage | 27 | |
| dc.identifier.trdizinid | 1356221 | |
| dc.identifier.uri | https://doi.org/10.53570/jnt.1732995 | |
| dc.identifier.uri | https://search.trdizin.gov.tr/tr/yayin/detay/1356221 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.12428/34017 | |
| dc.indekslendigikaynak | TR-Dizin | |
| dc.language.iso | en | |
| dc.relation.ispartof | Journal of New Theory | |
| dc.relation.publicationcategory | Makale - Ulusal Hakemli Dergi - Kurum Öğretim Elemanı | |
| dc.rights | info:eu-repo/semantics/openAccess | |
| dc.snmz | KA_TR_20260130 | |
| dc.subject | Prime $\\Gamma$-ideals | |
| dc.subject | $\\lvert P_{S_{\\Gamma}}\\rvert$-regular $\\Gamma$-semigroups | |
| dc.subject | $\\lvert P_{S_{\\Gamma}}\\rvert$-reduced $\\Gamma$-semigroups | |
| dc.subject | $\\lvert P_{S_{\\Gamma}}\\rvert$-idempotent $\\Gamma$-semigroups | |
| dc.subject | $\\lvert P_{S_{\\Gamma}}\\rvert$-strongly idempotent $\\Gamma$-semigroups | |
| dc.title | Source of ?-Semigroups’ Primeness | |
| dc.type | Article |
