14 citations · 50 across the 12 of their papers we have counts for
14 papers · 1 filter
Limit varieties of aperiodic monoids
Sergey V. Gusev, Olga B. Sapir
A limit variety is a variety that is minimal with respect to being non-finitely based. We present a new limit variety of aperiodic monoid. We also show that if there exists any oth…
Non-finitely related and finitely related monoids
Olga B. Sapir
We transform the method of Glasson into a sufficient condition under which a monoid is non-finitely related, add a new member to the collection of interlocking word-patterns, and u…
Strongly nonfinitely based monoids
Sergey V. Gusev, Olga B. Sapir, Mikhail V. Volkov
We show that the 42-element monoid of all partial order preserving and extensive injections on the 4-element chain is not contained in any variety generated by a finitely based fin…
Catalan monoids inherently nonfinitely based relative to finite -trivial semigroups
Olga B. Sapir, Mikhail V. Volkov
We show that the 42-element monoid of all partial order preserving and extensive injections on the 4-element chain is not contained in any variety generated by a finitely based fin…
Limit varieties generated by finite non-J-trivial aperiodic monoids
Olga B. Sapir
Jackson and Lee proved that certain six-element monoid generates a hereditarily finitely based variety whose lattice of subvarieties contains an infinite ascending ch…
Classification of limit varieties of J-trivial monoids
S. V. Gusev, O. B. Sapir
A variety of algebras is called limit if it is non-finitely based but all its proper subvarieties are finitely based. We present a new pair of limit varieties of monoids and show t…
Limit varieties of -trivial monoids
Olga B. Sapir
We show that limit varieties of monoids recently discovered by Gusev, Zhang and Luo and their subvarieties are generated by monoids of the form for certain congruences …
Lee monoid is non-finitely based
Inna Mikhailova, Olga Sapir
We establish a new sufficient condition under which a monoid is non-finitely based and apply this condition to show that the 9-element monoid is non-finitely based. The mon…
Lee monoids are non-finitely based while the sets of their isoterms are finitely based
Olga Sapir
We establish a new sufficient condition under which a monoid is non-finitely based and apply this condition to Lee monoids , obtained by adjoining an identity element to…
Finitely based sets of 2-limited block-2-simple words
Olga Sapir
Let be an alphabet and be a set of words in the free monoid . Let denote the Rees quotient over the ideal of consisting…
The finite basis problem for the monoid of 2 by 2 upper triangular tropical matrices
Yuzhu Chen, Xun Hu, Yanfeng Luo +1
For each positive , let denote the identity obtained from the Adjan identity by substituting $(xy) \rightarrow…
The finite basis problem for words with at most two non-linear variables
Olga Sapir
Let A be an alphabet and W be a set of words in the free monoid A*. Let S(W) denote the Rees quotient over the ideal of A* consisting of all words that are not subwords of words in…
Non-finitely based monoids
Olga Sapir
We present a general method for proving that a semigroup is non-finitely based. The method is strong enough to cover the non-finite basis arguments in articles [1,3,4,5,7,8, 11,14,…
Finitely based monoids
Olga Sapir
We present a method for proving that a semigroup is finitely based and find some new sufficient conditions under which a monoid is finitely based. As an application, we find a clas…