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Independent systems of generators and the Hopf property for unary algebras
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V. K. Kartashov
Published/Copyright:
December 9, 2008
Abstract
We introduce the notion of an independent set of elements of a unary algebra as a subset of its support, where in any pair of elements one element does not belong to the subalgebra generated by the other. It is proved that any two independent systems of generators of a unary algebra have the same cardinality. With the use of this assertion it is proved that any finitely generated unary algebra with commutative operations possesses the Hopf property: each epiendomorphism of the algebra is an automorphism.
Received: 2007-05-16
Published Online: 2008-12-09
Published in Print: 2008-December
© de Gruyter 2008
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Articles in the same Issue
- On stability of a vector combinatorial problem with MINMIN criteria
- On the asymptotic behaviour of the probability of existence of equivalent tuples with nontrivial structure in a random sequence
- Characteristics of random systems of linear equations over a finite field
- On the realisation of Boolean functions by informational graphs
- Estimates of the number of occurrences of vectors on cycles of linear recurring sequences over a finite field
- Finite generability of some groups of recursive permutations
- Independent systems of generators and the Hopf property for unary algebras
- Estimates of the complexity of approximation of continuous functions in some classes of determinate functions with delay
- On ranks, Green classes, and the theory of determinants of Boolean matrices
