Characterization of Pomonoids by Properties of I-Regular S-Posets

Tingting Zhao ()
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Tingting Zhao: College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China

Mathematics, 2025, vol. 13, issue 21, 1-17

Abstract: In 2005, Shi defined I-regular S-posets and used this concept to characterize P P -pomonoids and po-cancellable pomonoids. In this paper, we continued the development of the homological classification of pomonoids by using the I-regularity of S-posets. First, we characterized pomonoids over which all I-regular S-posets have one of the properties around projectivity or injectivity, and many known results were generalized. Moreover, some possible conditions on pomonoids that describe when their diagonal posets are I-regular were found. Finally, some characterizations of pomonoids by the I-regularity of their Rees factor posets were given.

Keywords: I-regular; S-poset; Rees factor; regular pomonoid (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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