Verjetnost komutativnosti v končnih kolobarjih : delo diplomskega seminarja

Kelaidis, Luka Iosif (author), Dolžan, David (mentor)

V tem diplomskem delu obravnavamo verjetnost komutativnosti končnih kolobarjev, ki predstavlja merilo, kako blizu je kolobar komutativni strukturi. Delo povzema in sistematizira obstoječe rezultate ter jih interpretira v kontekstu relativne verjetnosti komutativnosti podkolobarjev v končnih kolobarjih. Poleg tega obravnavamo tudi lastnosti Z-izoklinizma parov kolobarjev in dokažemo invarianco verjetnosti komutativnosti glede na Z-izoklinizem. Vključimo tudi nekaj primerov, ki ponazarjajo teoretične rezultate.

• Language: Slovenian
• Keywords: končen kolobar, verjetnost komutativnosti, izoklinizem kolobarjev
• Work type: Final seminar paper
• Typology: 2.11 - Undergraduate Thesis
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2026
• PID: 20.500.12556/RUL-187464
• UDC: 512
• COBISS.SI-ID: 290829315
• Publication date in RUL: 11.09.2026

Secondary language

• Language: English
• Title: Commuting probability of finite rings

Abstract

This thesis examines the commuting probability of finite rings, which serves as a measure of how close a ring is to a commutative structure. The thesis summarizes and systematizes existing results, interpreting them in the context of the relative commuting probability of subrings in finite rings. Additionally, it explores the properties of Z-isoclinism of pairs of rings and proves the invariance of commuting probability under Z-isoclinism. Several examples illustrate the theoretical results.

• Keywords: finite ring, commuting probability, isoclinism of rings