2017/06/04 by Alexandr Kazda, Kazda, Alexandr · 1 citation
Computer Science · Mathematics · #08B05 #Advanced Algebra and Logic #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Logic (math.LO) #Rings and Algebras (math.RA) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.1706.01147
openalex publication_date 2017/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is known that any finite idempotent algebra that satisfies a nontrivial\nMaltsev condition must satisfy the linear one-equality Maltsev condition (a\nvariant of the term discovered by M. Siggers and refined by K. Kearnes, P.\nMarkovi 'c, and R. McKenzie):\n n t(r,a,r,e)
approx t(a,r,e,a).\n We show that if we drop the finiteness assumption, the k-ary weak near\nunanimity equations imply only trivial linear one-equality Maltsev conditions\nfor every k\≥ 3. From this it follows that there is no nontrivial linear\none-equality condition that would hold in all idempotent algebras having Taylor\nterms.\n Miroslav Ol vs 'ak has recently shown that there is a weakest nontrivial\nstrong Maltsev condition for idempotent algebras. Ol vs 'ak has found several\nsuch (mutually equivalent) conditions consisting of two or more equations. Our\nresult shows that Ol vs 'ak's equation systems can't be compressed into just\none equation.\n