Abstract
The constant mappings onto the unit form a zero subcategory of any category of monoid homomorphisms; a varietyV of monoids isalmost universal if every category of algebras is isomorphic to a class of all nonzero homomorphisms between members ofV. Almost universal monoid varieties are shown to be exactly those varieties containing all commutative monoids in which the identity xnyn=(xy)n fails for every n>1. Almost universal varieties of monoids can also be characterized categorically as the varieties containing all groups with zero as one-object full subcategories.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Yuji Kobayashi,On the structure of exponent semigroups, J. Alg.78 (1982), 1, 1–19.
V.Koubek and J.Sichler,Universal varieties of semigroups, to appear in Austr. J. Math, in print.
L. Kucera,On the monoids of homomorphisms of semigroups with unity, Comment. Math. Univ. Carolinae23 (1982), 369–381.
A.Pultr and V.Trnkovä,Combinatorial, Algebraic and Topological Representations of Groups,Semigroups and Categories, North Holland 1980.
Author information
Authors and Affiliations
Additional information
The support of NSERC is gratefully acknowledged.
Rights and permissions
About this article
Cite this article
Koubek, V., Sichler, J. Almost universal varieties of monoids. Algebra Universalis 19, 330–334 (1984). https://doi.org/10.1007/BF01201100
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF01201100