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RESULTS ON FINITE SEMIGROUPS DERIVED FROM THE ALGEBRAIC THEORY OF MACHINES

K. Krohn, J. Rhodes
1965 Proceedings of the National Academy of Sciences of the United States of America  
Prime Decomposition 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.  ... 
doi:10.1073/pnas.53.3.499 pmid:16591264 pmcid:PMC336965 fatcat:afrdeeuujza5joi2k4febmt57i

Symmetric inverse topological semigroups of finite rank ≤ n

O. V. Gutik, A. R. Reiter
2010 Journal of Mathematical Sciences  
Let : k hS l ® J be arbitrary 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.  ... 
doi:10.1007/s10958-010-0147-z fatcat:3pzfg2sm5zbu3lc46kh6narqtq

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  ... 

Maximal homomorphic images of commutative semigroups

D. B. McAlister, L. O'Carroll
1971 Glasgow Mathematical Journal  
Now, it is immediate from the structure 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.  ... 
doi:10.1017/s0017089500001087 fatcat:bjodlujzrrbcdcz7cq5q6h4k44

Finitely generated steady $\mathfrak{N}$-semigroups

Takayuki Tamura
1973 Proceedings of the American Mathematical Society  
also studies the 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.  ... 
doi:10.1090/s0002-9939-1973-0327957-5 fatcat:mwjvgqf325gd7nhkcgjvbrfaye

Representing N-semigroups

John C. Higgins
1969 Bulletin of the Australian Mathematical Society  
This paper obtains 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 .  ... 
doi:10.1017/s0004972700041320 fatcat:ikjmnrfzi5dibldsd3x6r4sr5e

On a problem of Baayen and Kruyswijk

D. A. Burgess
1968 Proceedings of the Edinburgh Mathematical Society  
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.  ...  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.  ... 
doi:10.1017/s0013091500012529 fatcat:jwm3btvcijavxeh74f6jgasr5y

Hales-Jewett type configurations in small sets [article]

Aninda Chakraborty, Sayan Goswami
2021 arXiv   pre-print
In 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.  ... 
arXiv:2009.00772v2 fatcat:wh4kjfrdqbbizbsk3meihy4zni

The left-discrimination sequence of an automaton

William R. Edwards, Zamir Bavel
1978 Information and Control  
This sequence is shown to be preserved by 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,  ... 
doi:10.1016/s0019-9958(78)90227-9 fatcat:cki7rezylba4zkcq3vkocsrtie

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

I. Protasov, J. Pym, D. Strauss
2000 Topology and its Applications  
The second main result shows that many continuous 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.  ... 
doi:10.1016/s0166-8641(99)00061-9 fatcat:44wvr2qgabeybdprslzheq6e5q

On locally finite semigroups

T. K. Brown
1969 Ukrainian Mathematical Journal  
H is 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.  ... 
doi:10.1007/bf01085231 fatcat:er3rshoycbdkfki7b3yphnucqq

Automaton semigroup free products revisited [article]

Tara Brough
2020 arXiv   pre-print
The result is extended by induction to give 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  ... 
arXiv:2003.12810v1 fatcat:j6eikh654rhi7bhpeb6sbr5dci

On the Decidability of Iterated Semidirect Products with Applications to Complexity

Jorge Almeida, Benjamin Steinberg
2000 Proceedings of the London Mathematical Society  
Roughly speaking, the decidability of 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).  ... 
doi:10.1112/s0024611500012144 fatcat:jf2eqtegpjfr5jrb5rdawnyncm

E-varieties and E-pseudovarieties of regular semigroups

Monica Mangold
1996 Bulletin of the Australian Mathematical Society  
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.  ...  (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.  ... 
doi:10.1017/s0004972700017068 fatcat:kg2uzmgmibeerkgyuxrc2zxnbi
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