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On right units of special inverse monoids
Igor Dolinka, Robert D. Gray
We study the class of monoids that arise as the submonoid of right units of finitely presented special inverse monoids (SIMs). Gray and Ruškuc (2024) gave the first example of a fi…
Semiring and involution identities of powers of inverse semigroups
Igor Dolinka, Sergey V. Gusev, Mikhail V. Volkov
The set of all subsets of any inverse semigroup forms an involution semiring under set-theoretical union and element-wise multiplication and inversion. We find structural condition…
Prefix monoids of groups and right units of special inverse monoids
Igor Dolinka, Robert D. Gray
A prefix monoid is a finitely generated submonoid of a finitely presented group generated by the prefixes of its defining relators. Important results of Guba (1997), and of Ivanov,…
Free idempotent generated semigroups: The word problem and structure via gain graphs
Igor Dolinka
Building on the previous extensive study of Yang, Gould and the present author, we provide a more precise insight into the group-theoretical ramifications of the word problem for f…
New results on the prefix membership problem for one-relator groups
Igor Dolinka, Robert D. Gray
In this paper we prove several results regarding decidability of the membership problem for certain submonoids in amalgamated free products and HNN extensions of groups. These gene…
Sandwich semigroups in diagram categories
Ivana Đurđev, Igor Dolinka, James East
This paper concerns a number of diagram categories, namely the partition, planar partition, Brauer, partial Brauer, Motzkin and Temperley-Lieb categories. If denotes a…