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|2 (.971, ,99-225) A.L Shmel'kin AMS 1980 Subject Classification: 20E25 |
LOCALLY FINITE SEMI-GROUP - A semi-group in which every finitely-generated
sub-semi-group is finite. A locally finite semi-group is a periodic semi-group (
|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].
|Samuel Eilenberg. 4. Locally Finite Monoids In trying to define the class Rat]; S |
when S is a semigroup and K is a commutative semiring not assumed to be
complete we encounter the following difficulties. The formula ...
|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. Proof. Suppose that the
ideal SES is not locally finite, so there exists a finite number of elements sieis′i ...
|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 ...
Leonid A. Bokut, Anatoliĭ Ivanovich Malʹt︠s︡ev, Alekseĭ Ivanovich Kostrikin - 1992 - Preview - More editions
|Let R be a variety in which all nil semigroups and all groups are locally finite. |
Suppose TI does not contai n BA. Then R is locally -finite. PROOF. Take such a
variety ft and a semigroup S in R. Since every group -from R is locally finite, ...
|(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*, ...
|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 ...
|Let T be a finite semigroup and ,p : S , T be a surjective homomorphism such |
that ^"1(e) is locally finite for every idempotent e £ T. Let X be a finite subset of 5,
F be the free semigroup on X, n : F , S be the identity on X, and ip = ,p o n ; F
|We use the following result. A semigroup S is called locally finite if each finite |
subset of S generates a finite subsemigroup. Theorem 3.6 (Brown 197 1 ) Let <p :
S > T be a morphism of a semigroups S onto a locally finite semigroup T. If the