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RESULTS ON FINITE SEMIGROUPS DERIVED FROM THE ALGEBRAIC THEORY OF MACHINES

1965
*
Proceedings of the National Academy of Sciences of the United States of America
*

Prime Decomposition

doi:10.1073/pnas.53.3.499
pmid:16591264
pmcid:PMC336965
fatcat:afrdeeuujza5joi2k4febmt57i
*Theorem**for**Finite**Semigroups*.-In this note, all*semigroups*are of*finite*order. ... One*semigroup*S1 is said to divide another*semigroup*S2, written Sij S2, iff S1 is*a**homomorphic*image of*a*subsemigroup S C S2. ... Prime Decomposition*Theorem**for**Finite**Semigroups*.-In this note, all*semigroups*are of*finite*order. ...##
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Symmetric inverse topological semigroups of finite rank ≤ n

2010
*
Journal of Mathematical Sciences
*

Let : k hS l ® J be arbitrary

doi:10.1007/s10958-010-0147-z
fatcat:3pzfg2sm5zbu3lc46kh6narqtq
*homomorphism*from k l J with the discrete topology into*a*topological*semigroup*S with countably compact square SŚ . ... Then by*Theorem*4 the restriction 1 : hS l l ® J J of*homomorphism*h onto the subsemigroup 1 l J of k l J is an annihilating*homomorphisms*. Let 11 1 ()() hhe ll l == J JJ ...*A**semigroup**homomorphism*: hST ® is called annihilating if () sh= () th =*for*all , stS Î .*A*This completes the proof of the*theorem*. àTheorem 5 implies*Theorem*6. ...##
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Page 815 of Mathematical Reviews Vol. 38, Issue 5
[page]

1969
*
Mathematical Reviews
*

*A*

*semigroup*8 is

*homomorphically*

*finite*if S is infinite and each noninjec- tive

*homomorphism*has

*finite*range. ... Two conditions, each equiva- lent to the existence of

*a*homogeneous

*homomorphism*of

*a*given

*semigroup*, are stated, as is

*a*

*theorem*that every

*homomorphism*of

*a*

*semigroup*S onto

*a*

*semigroup*7' can be extended ...

##
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Maximal homomorphic images of commutative semigroups

1971
*
Glasgow Mathematical Journal
*

Now, it is immediate from the structure

doi:10.1017/s0017089500001087
fatcat:bjodlujzrrbcdcz7cq5q6h4k44
*theorem**for**finite*commutative groups [2,*Theorem*10.1] that*a**finite*commutative group, which has*a*minimum non-trivial subgroup, is cyclic of prime power order ... Hence H{*a*) is/7-primary*for*each aeG, and so Gis/7-primary.*THEOREM*Let S be*a*commutative*semigroup*. ... However, if*a*commutative*semigroup*obeys certain*finiteness*conditions,*for*example if it is*finitely*generated, then it has*a*maximal group*homomorphic*image if and only if it is £-inversive. ...##
###
Finitely generated steady $\mathfrak{N}$-semigroups

1973
*
Proceedings of the American Mathematical Society
*

also studies the

doi:10.1090/s0002-9939-1973-0327957-5
fatcat:mwjvgqf325gd7nhkcgjvbrfaye
*homomorphisms*of*a**finitely*generated steady 9Z-*semigroup*into another. ... In this paper the author proves that S is*a**finitely*generated steady Si-*semigroup*if and only if S is isomorphic to the direct product of*a**finite*abelian group and the infinite cyclic*semigroup*; and ... In-this paper we treat only*finitely*generated ^-*semigroups*.*Theorem*6. Let S=(G;1) be*a**finitely*generated 9Î-*semigroup*. ...##
###
Representing N-semigroups

1969
*
Bulletin of the Australian Mathematical Society
*

This paper obtains

doi:10.1017/s0004972700041320
fatcat:ikjmnrfzi5dibldsd3x6r4sr5e
*a*representation of*finitely*generated W-*semigroups*as the subdirect product of an abelian group and*a*subsemigroup of the additive positive integers. ... An ^-*semigroup*is*a*commutative, cancellative, archimedean*semigroup*with no idempotent element. ... Then*a**semigroup*T has*a*greatest*homomorphic*image of type F if:*THEOREM*4. 2 2 Every*semigroup*, T , has*a*greatest homomorphia image of type r . ...##
###
On a problem of Baayen and Kruyswijk

1968
*
Proceedings of the Edinburgh Mathematical Society
*

Finally in section 5 I give the weaker

doi:10.1017/s0013091500012529
fatcat:jwm3btvcijavxeh74f6jgasr5y
*theorem*that every*finite*commutative*semigroup*is*a**homomorphic*image of an arithmetical*semigroup*. 2. Let S be*a**finite*commutative*semigroup*. ... In section 21 obtain*a*necessary and sufficient condition*for**a**finite**semigroup*to be arithmetical. ... Finally in section 5 I give the weaker*theorem*that every*finite*commutative*semigroup*is*a**homomorphic*image of an arithmetical*semigroup*. 2. Let S be*a**finite*commutative*semigroup*. ...##
###
Hales-Jewett type configurations in small sets
[article]

2021
*
arXiv
*
pre-print

In

arXiv:2009.00772v2
fatcat:wh4kjfrdqbbizbsk3meihy4zni
*a*recent work, N. Hindman, D. Strauss and L. Zamboni have shown that the Hales-Jewett*theorem*can be combined with*a*sufficiently well behaved*homomorphisms*. ... Their work was completely algebraic in nature, where they have used the algebra of Stone-Cech compactification of discrete*semigroup*. ... Dibyendu De*for*his helpful comments on this paper. ...##
###
The left-discrimination sequence of an automaton

1978
*
Information and Control
*

This sequence is shown to be preserved by

doi:10.1016/s0019-9958(78)90227-9
fatcat:cki7rezylba4zkcq3vkocsrtie
*homomorphisms*and is extended and used in an algorithm*for*determining the*homomorphisms*on one*finite*automaton to another. utility (e.g., Deussen, 1966; Dragan ... is*finite*. ...*Theorem*1 points out the appropriateness of the name*for*this sequence, since J~+l = J~*for**finite**A*if and only if J~ is left-discriminative, and J~+l is*a*proper*homomorphic*image of J~ as long as J, ...##
###
Page 1042 of Mathematical Reviews Vol. 39, Issue 5
[page]

1970
*
Mathematical Reviews
*

Let

*A*be*a**semigroup*and ¢*a*set of*homomorphisms*of*A*into*finite**semigroups*. ... In the last section ¢ is the set of all*homomorphisms*of*A*into*finite**semigroups*. ...##
###
A lemma on extending functions into F -spaces and homomorphisms between Stone–Čech remainders

2000
*
Topology and its Applications
*

The second main result shows that many continuous

doi:10.1016/s0166-8641(99)00061-9
fatcat:44wvr2qgabeybdprslzheq6e5q
*homomorphisms*from S * to G * have to arise from*homomorphisms*mapping S to G, where S is*a*discrete*semigroup*and G is*a*discrete group and S * denotes ... βS of*a*discrete*semigroup*S. ... This example also shows that the observation in Example 4.2(i) that any*homomorphism*from S * to*a**finite*group is generated by*a**homomorphism*from S to the group, does not extend to*finite**semigroups*. ...##
###
On locally finite semigroups

1969
*
Ukrainian Mathematical Journal
*

H is

doi:10.1007/bf01085231
fatcat:er3rshoycbdkfki7b3yphnucqq
*a**homomorphism*of the group G onto the locally*finite*group H with locally*finite*kernel, then G is locally*finite*. In this paper we prove the exact analogue of this*theorem**for**semigroups*. ... Then in the last section we give several consequences, including the well-known*theorem*of Shevrin which states that*a*band of locally*finite**semigroups*is locally*finite*, and the*theorem*of Green and ... Let T be*a**finite**semigroup*and suppose the*theorem*holds*for*all*semigroups*T H with jT H j < jTj. ...##
###
Automaton semigroup free products revisited
[article]

2020
*
arXiv
*
pre-print

The result is extended by induction to give

arXiv:2003.12810v1
fatcat:j6eikh654rhi7bhpeb6sbr5dci
*a*condition*for**a*free product of*finitely*many automaton*semigroups*to be an automaton*semigroup*. ... An improvement on earlier results on free products of automaton*semigroups*; showing that*a*free product of two automaton*semigroups*is again an automaton*semigroup*providing there exists*a**homomorphism*... Acknowledgements The author was supported by the Fundação para*a*Ciência e*a*Tecnologia ...##
###
On the Decidability of Iterated Semidirect Products with Applications to Complexity

2000
*
Proceedings of the London Mathematical Society
*

Roughly speaking, the decidability of

doi:10.1112/s0024611500012144
fatcat:jf2eqtegpjfr5jrb5rdawnyncm
*a*semidirect product follows from*a*mild, commonly verified property of the first factor plus the stronger property*for*all the other factors. ... aperiodic*semigroups*, thereby suggesting*a*new approach to answer (affirmatively) the question as to whether complexity is decidable. ... McCammond, they could prove that*A*is κ-reducible and κ-recursive (compare with*Theorem*5.12). ...##
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E-varieties and E-pseudovarieties of regular semigroups

1996
*
Bulletin of the Australian Mathematical Society
*

An e-pseudovariety is defined to be

doi:10.1017/s0004972700017068
fatcat:kg2uzmgmibeerkgyuxrc2zxnbi
*a*class of*finite*regular*semigroups*closed under the formation of*homomorphic*images, regular subsemigroups and*finite*direct products. ... (*A*similar result is given*for*locally inverse*finite*regular ... An e-pseudovariety is defined to be*a*class of*finite*regular*semigroups*closed under the formation of*homomorphic*images, regular subsemigroups and*finite*direct products. ...
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