Semigroup of weak endomorphisms of a partial equivalence relationship

• Дата: 2025
• Автори: Zhuchok, Yu., Toichkina, О., Жучок, Юрій, Тоічкіна, Олена
• Формат: Стаття
• Мова: Українська
• Опубліковано: Institute of Mathematics, NAS of Ukraine 2025
• Онлайн доступ: https://umj.imath.kiev.ua/index.php/umj/article/view/8412
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

UDC 512.53 We study the weak endomorphism semigroup of a  partial equivalence relation. We describe necessary and sufficient conditions for the existence  of these endomorphisms and, in general, endotopisms. We establish the conditions under which the set of all idempotents of the weak endomorphism semigroup of a strict partial equivalence is its subsemigroup, as well as the conditions of regularity and coregularity of the weak endomorphism semigroup. In terms of the wreath product of a symmetric transformation semigroup and a small category,  we describe a faithful representation of the weak endomorphism semigroup of an arbitrary relation of a strict partial equivalence.