About 43,500 results
|Examples of varieties of semi-groups with finite bases are: any variety of |
commutative semi-groups; any periodic ... finite semi-groups) if and only if the
variety of all groups in "Si is locally finite: the small locally finite varieties of
groups are ...
|The proof of the next lemma employs uniformly recurrent bi-infinite words again. |
Lemma 3.6.32. Let E be the set of all idempotents of a semigroup S. If each
subsemigroup eSe, e ∈ E, is locally finite, then the ideal SES is locally finite.
|Let G be a group and let F be a field. Then F[G] is regular if and only if G is locally |
finite and F has characteristic 0 or a prime that is not the order of an element of G.
Regularity of semigroup algebras was first investigated by Weissglass [BH].
|A semigroup is said to be periodic if each of its one-generated subsemigroups is |
finite and locally finite if each of its finitely generated subsemigroups is finite. A
variety of semigroups is locally finite if all its members are locally finite. Let A and
|(The results for groups are, of course, special cases of the semigroup results.) A |
semigroup S is said to be locally finite if every finitely generated subsemigroup of
S is finite. I will say that S is strongly locally finite if there is a function f : Z * -- Z*, ...
|A finite nil semi-group is nilpotent, and the classes of locally nilpotent semi-|
groups and locally finite nil semi-groups coincide (see Locally finite semi-group).
An even narrower class is formed by the semi-groups with an ascending
|Note that K [S; 6] is isomorphic to the semigroup E-algebra K [S] if and only if 6 is |
a coboundary. Not unexpectedly more information is obtained when the
semigroup is finite and we now turn our attention to this case. A semigroup is
locally finite ...
|A classical result of Zorn shows that finite groups satisfying an Engel identity are |
nilpotent. ... SEMIGROUP IDENTITIES We note that some other group identities
can be studied by combining Zelmanov's work with the theory of powerful ...
|The language of pseudova- rieties serves as the unifying organizational principle |
in Finite Semigroup Theory. ... one can write down with both sides having length
at most 3, and every subpseudovariety of the locally finite pseudovariety of ...
|Many authors have contributed to this task, in the end determining the existence |
of finite bases of identities for all semigroups of these orders. Variety generated
by the semigroup (6) is essentially infinitely based, in the sense that no locally ...