Abstract
We first obtain several subdirect product decompositions of additively regular semirings by constructing several pairs of generalized factor congruences. Next, we define and study several additively regular semiring varieties by congruence openings and closure congruences. Moreover, as an application, we obtain several pullback product decompositions of additively regular band semirings. Finally, we establish order embedding theorems on the poset of subvarieties of the additively regular semiring e-variety \(\mathscr{A}\mathscr{R}\).
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This paper is supported by Grants of Natural Science Foundation of China (11971383, 11801239) and a Grant of Shaanxi Fundamental Science Research Project for Mathematics and Physics (22JSY023).
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Xian, X., Shao, Y. Subdirect product decompositions of additively regular semirings. Soft Comput 28, 51–60 (2024). https://doi.org/10.1007/s00500-023-09150-4
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DOI: https://doi.org/10.1007/s00500-023-09150-4