Open AccessТопологические решеточно упорядоченные кольца с AM-свойством
Author(s) -
Omid Zabeti
Publication year - 2021
Publication title -
vladikavkazskij matematičeskij žurnal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.126
H-Index - 2
eISSN - 1814-0807
pISSN - 1683-3414
DOI - 10.46698/a8913-4331-4311-d
Subject(s) - bounded function , homomorphism , mathematics , pure mathematics , lattice (music) , lebesgue integration , property (philosophy) , order (exchange) , discrete mathematics , mathematical analysis , physics , philosophy , epistemology , finance , acoustics , economics
Motivated by the recent definition of the $AM$-propertyin locally solid vector lattices [O. Zabeti, doi:10.1007/s41980-020-00458-7], in this note, we try to investigatesome counterparts of those results in the category of all locallysolid lattice rings. In fact, we characterize locally solid latticerings in which order bounded sets and bounded sets agree.Furthermore, with the aid of the $AM$-property, we find conditionsunder which order bounded group homomorphisms and different types ofbounded group homomorphisms coincide. Moreover, we show that eachclass of bounded order bounded group homomorphisms on a locallysolid lattice ring $X$ has the Lebesgue or the Levi property if andonly if so is $X$.