PreprintCC BY 4.0arXiv
Subvariety intervals and limit varieties of zero extensions of mirror-word semirings
Abstract
For the mirror word mn=a1⋯ anan⋯ a1, let 𝒱n=V(S(mn)) and 𝒲n=V(S(mn)0). We show that [𝒲n,𝒲n+1] (n≥ 1) and [𝒱n,𝒲n] (n≥ 2) have cardinality 2ℵ0. Every variety in [𝒲2,𝒲∞] has infinite axiomatic rank. The unique limit subvariety of 𝒲1 is V(SR6). For n≥ 2, we construct a distinct directed-path limit variety contained in 𝒲n but not in 𝒱n.
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BibTeX
@misc{wang2026subvariety,
title = {{Subvariety intervals and limit varieties of zero extensions of mirror-word semirings}},
author = {Ruijing Wang and Mengya Yue},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.23478},
eprint = {2610.23478},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.23478},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Subvariety intervals and limit varieties of zero extensions of mirror-word semirings
AU - Ruijing Wang
AU - Mengya Yue
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2610.23478
UR - https://arxiv.org/abs/2610.23478
AB - For the mirror word m_n=a_1⋯ a_na_n⋯ a_1, let 𝒱_n=V(S(m_n)) and 𝒲_n=V(S(m_n)^0). We show that [𝒲_n,𝒲_n+1] (n≥ 1) and [𝒱_n,𝒲_n] (n≥ 2) have cardinality 2^ℵ_0. Every variety in [𝒲_2,𝒲_∞] has infinite axiomatic rank. The unique limit subvariety of 𝒲_1 is V(SR_6). For n≥ 2, we construct a distinct directed-path limit variety contained in 𝒲_n but not in 𝒱_n.
ER -