Cyclic subgroupoids of an absolutely free groupoid
Journal
Proceedings of III Congress of Mathematicians of Macedonia, Struga, R. Macedonia, 29.IX.2005-2.X.2005
Date Issued
2007
Author(s)
Celakoska-Jordanova, Vesna
Abstract
Subgroupoids of an absolutely free groupoid F = (F,⋅) with a
free basis B that are generated by one element (called cyclic
subgroupoids of F ) are considered. It is shown that: two cyclic
subgroupoids of F have common elements if and only if one of them is
contained in the other; F has maximal cyclic subgroupoids and if
card(B) ≥ 2 , every cyclic subgroupoid is contained in a maximal one; any two
maximal cyclic subgroupoids of F are either disjoint or equal. Also, a
characterization of maximal cyclic subgroupoids of F by means of
primitive elements in F is given. This statements are also true for an
absolutely free groupoid with one-element basis (with modified
definition of maximal cyclic subgroupoid).
free basis B that are generated by one element (called cyclic
subgroupoids of F ) are considered. It is shown that: two cyclic
subgroupoids of F have common elements if and only if one of them is
contained in the other; F has maximal cyclic subgroupoids and if
card(B) ≥ 2 , every cyclic subgroupoid is contained in a maximal one; any two
maximal cyclic subgroupoids of F are either disjoint or equal. Also, a
characterization of maximal cyclic subgroupoids of F by means of
primitive elements in F is given. This statements are also true for an
absolutely free groupoid with one-element basis (with modified
definition of maximal cyclic subgroupoid).
Subjects
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