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math.GR2026
An explicit construction of a limit variety of groups
Zidong Gao, Yilin Zhou
We construct an explicit countable group \(G_*=N(R)\rtimes A\) whose generated variety is a limit variety of groups: it has no finite identity basis, whereas every proper subvariet…
math.GR2026
Equational Theories of Interval Semirings of Posets
Zidong Gao, Yilin Zhou
We study the equational theory and subvariety structure of the ai-semiring variety $\V_\infty$ generated by all flat semirings , where the letters \(a_i\) are pai…
math.GR2026
The finite basis problem for flat semirings , and
Zidong Gao, Miaomiao Ren, Yilin Zhou
We study the finite basis problem for flat semirings of the forms \(S_c(W)\), \(M_c(W)\), and \(M(W)\), where \(W\) is a nonempty set of words in a free commutative semigroup, a fr…