zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Prime decomposition theorem for arbitrary semigroups: General holonomy decomposition and synthesis theorem. (English) Zbl 0679.20056
The authors generalize the holonomy form of the Prime Decomposition Theorem of Krohn and Rhodes for finite semigroups to arbitrary infinite semigroups. This is accomplished by embedding $\hat S$ into an infinite Zeiger wreath product after applying the triple Schützenberger product which makes S finite-J-above (Rhodes’ theorem). Here finite-J-above means every element has only a finite number of divisors.
Reviewer: L.Potemkin

20M10General structure theory of semigroups
20M50Connections of semigroups with homological algebra and category theory
20M05Free semigroups, generators and relations, word problems
Full Text: DOI
[1] Arbib, M. A.: Languages and semigroups. (1968) · Zbl 0181.01501
[2] Birget, J. C.: The synthesis theorem for finite regular semigroups and its generalization. J. pure appl. Algebra 55, 1-79 (1988) · Zbl 0657.20050
[3] Birget, J. C.: Structure of finite semigroups and generalizations. Proc. 1984 marquette conference on semigroups (1984) · Zbl 0547.20054
[4] Birget, J. C.: Iteration of expansions - unambiguous semigroups. J. pure appl. Algebra 34, 1-55 (1984) · Zbl 0547.20054
[5] Birget, J. C.; Rhodes, J. L.: Almost finite expansions of arbitrary semigroups. J. pure appl. Algebra 32, 239-287 (1984) · Zbl 0546.20055
[6] Clifford, A. H.; Preston, G. B.: The algebraic theory of semigroups. (1961) · Zbl 0111.03403
[7] Eilenberg, S.: Automata, languages and machines. (1976) · Zbl 0359.94067
[8] Henckell, K.: Pointlike sets: the finest aperiodic cover of a finite semigroup. J. pure appl. Algebra 55, 85-126 (1988) · Zbl 0682.20044
[9] Lallement, G.: Semigroups and combinatorial applications. (1979) · Zbl 0421.20025
[10] Pin, J. E.: Varieties of formal languages. (1984)
[11] Rhodes, J.: Infinite iteration of matrix semigroups, part I: Structure theorem for torsion semig-groups. J. algebra 98, 422-451 (1986) · Zbl 0584.20053
[12] Rhodes, J.: Infinite iteration of matrix semigroups, part II: Structure theorem for arbitrary semi-groups up to aperiodic morphism. J. algebra 100, 25-137 (1986) · Zbl 0626.20050
[13] Rhodes, J.; Jr., D. Allen: Synthesis of the classical and modern theory of finite semigroups. Adv. math. 11, 238-266 (1973)
[14] J. Rhodes and B. Tilson, The kernel of monoid morphisms, to be published. · Zbl 0698.20056