5 papers
The Finite Basis Problem for Semirings of Order Four
Aifa Wang, Lili Wang, Qingrui Yin +1
The finite basis problem for small semirings differs from its semigroup counterpart even in order three. Recent work classifies several additive types of four-element additively id…
A separating identity for matrix semirings over
Lili Wang, Jiewei Zhang, Aifa Wang
Jiao and Ren proved that the varieties generated by the matrix semirings $\M_n(S_7)$ form an ascending chain of nonfinitely based varieties, and asked whether consecutive members a…
The strong nonfinite basis property of
Lili Wang, Qingrui Yin, Aifa Wang
We prove that the three-element additively idempotent semiring is strongly nonfinitely based: every finite additively idempotent semiring whose generated variety contains $S_…
Compatible additions on a six-element commutative semigroup: equational bases and subvariety lattices
Lili Wang, Jinjing Wu, Aifa Wang
Let be the six-element commutative semigroup occurring as the common multiplicative reduct of the semirings and . The closing paragraph of Shao, Ren, and Gao~\cite…
On the variety generated by all semirings of order two
Aifa Wang, Lili Wang
There are ten distinct two-element semirings up to isomorphism, denoted \( L_2, R_2, M_2, D_2, N_2, T_2, Z_2, W_2, Z_7 \), and \( Z_8 \) (see \cite{bk}). Among these, the multiplic…