Author:
Wang Lili, ,Wang Aifa,Li Peng
Abstract
<abstract><p>We study the semiring variety generated by $ B^{0}, (B^{0})^{\ast}, A^{0}, N_{2}, T_{2}, Z_2, W_2 $. We prove that this variety is finitely based and prove that the lattice of subvarieties of this variety is a distributive lattice of order 2327. Moreover, we deduce this variety is hereditarily finitely based.</p></abstract>
Publisher
American Institute of Mathematical Sciences (AIMS)
Reference16 articles.
1. S. Burris, H. P. Sankappanavar, A Course in Universal Algebra, New York: Springer, 1981.
2. R. El Bashir, T. Kepka, Congruence-simple semirings, Semigroup Forum, 75 (2007), 588–608. https://doi.org/10.1007/s00233-007-0725-7
3. P. Gajdoš, M. Kuřil, On free semilattice-ordered semigroups satisfying $x^n\approx x$, Semigroup Forum, 80 (2010), 92–104. https://doi.org/10.1007/s00233-009-9188-3
4. S. Ghosh, F. Pastijn, X. Z. Zhao, Varieties generated by ordered bands Ⅰ, Order, 22 (2005), 109–128. https://doi.org/10.1007/s11083-005-9011-z
5. J. S. Golan, The theory of semirings with applications in mathematics and theoretical computer science, Harlow: Longman Scientific and Technical, 1992.