Open AccessAdditively orthodox semirings with special transversals
Author(s) -
Kaiqing Huang,
AUTHOR_ID,
Yizhi Chen,
Miaomiao Ren,
AUTHOR_ID,
AUTHOR_ID,
AUTHOR_ID
Publication year - 2022
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2022230
Subject(s) - semiring , mathematics , transversal (combinatorics) , semigroup , combinatorics , kleene algebra , algebra over a field , pure mathematics , discrete mathematics , mathematical analysis
A semiring $ (S, +, \cdot) $ is called additively orthodox semiring if its additive reduct $ (S, +) $ is a orthodox semigroup. In this paper, by introducing some special semiring transversals as the tools, the constructions of additively orthodox semirings with a skew-ring transversal or with a generalized Clifford semiring transversal are established. Meanwhile, it is shown that an additively orthodox semiring with a generalized Clifford semiring transversal is a b-lattice of additively orthodox semirings with skew-ring transversals. Consequently, the corresponding results of Clifford semirings and generalized Clifford semirings in reference (M. K. Sen, S. K. Maity, K. P. Shum, Clifford semirings and generalized Clifford semirings, Taiwan. J. Math., 9 (2005), 433–444) and completely regular semirings in reference (S. K. Maity, M. K. Sen, K. P. Shum, On completely regular semirings, Bull. Cal. Math. Soc., 98 (2006), 319–328) are extended and strengthened.