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Page 2129 of Mathematical Reviews Vol. , Issue 83e
[page]

1983
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Mathematical Reviews
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We characterize all

*subdirectly**irreducible**commutative**automata*and hence all*subdirectly**irreducible**commutative*semigroups as well.” Imreh, B. 83e:68068 On finite nilpotent*automata*. ... .; Imreh, B. 83¢:68067*Subdirectly**irreducible**commutative**automata*. Acta Cybernet. 5 (1980/81), no. 3, 251-260. Authors’ summary: “M. ...##
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Page 6188 of Mathematical Reviews Vol. , Issue 2000i
[page]

2000
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Mathematical Reviews
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Finally we characterize all finite

*subdirectly**irreducible*SIE-groupoids in V>;.” Miklés Csikés (G6d6116) 2000i:20109 20N05 Sandu, N. I. On the Bruck-Slaby theorem for*commutative*Moufang loops. ... We describe all*subdirectly**irreducible*groupoids in each nontrivial subvariety of the variety SIE of all SIE-groupoids. ...##
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Page 1428 of Mathematical Reviews Vol. 51, Issue 5
[page]

1976
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Mathematical Reviews
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A graph may admit several representations as a subdirect product of

*subdirectly**irreducible*graphs; it is shown that at least one representation is pure (i.e., the*subdirectly**irreducible*factors are all ... The*subdirectly**irreducible*graphs are of two kinds: the complete graphs and the almost complete graphs (i.e., with one edge missing). ...##
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Page 6888 of Mathematical Reviews Vol. , Issue 98K
[page]

1998
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Mathematical Reviews
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After an introductory section, Section 2 characterizes

*subdirectly**irreducible*semigroups of the various kinds of interest. ... Theo- rem 4.3: A variety of*commutative*semigroups is*subdirectly*dom- inated iff it is a 1-cancellative variety consisting of nil-semigroups. ...##
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Page 3262 of Mathematical Reviews Vol. , Issue 87f
[page]

1987
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Mathematical Reviews
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It is always

*subdirectly**irreducible*. If C is finite then syn(C) can be characterized as a*subdirectly**irreducible*finite nil monoid with at least three elements. ... Papers on*automata*and languages, VI, 77-87, DM, 84-3, Karl Marz Univ. Econom., Budapest, 1984. M. Szijarté (Fund. ...##
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The semiring variety generated by any finite number of finite fields and distributive lattices

2015
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Publications de l'Institut Mathématique (Beograd)
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. , F k are the only

doi:10.2298/pim150404026s
fatcat:6h2k3xzfcbhqfkgp2ojrpwani4
*subdirectly**irreducible*semirings in V. ... By Theorem 2.4 (ii) we immediately have that, up to isomorphism, there are finitely many*subdirectly**irreducible*members in V. Let T denote the set of all*subdirectly**irreducible*members in V. ... This shows that every*subdirectly**irreducible*semiring of V ′ is in V 2 and so V ′ = V 2 . This means that V 2 is finitely based. ...##
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Page 2829 of Mathematical Reviews Vol. , Issue 82g
[page]

1982
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Mathematical Reviews
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The author’s characterization of

*subdirectly**irreducible**commutative*BCK-algebras satisfying E,, follows also from results of that paper. ... (The class of all*automata*which have the property P, V(P), is a strong class if V(P) is closed under homomorphisms.)” ...##
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The variety of semirings generated by distributive lattices and finite fields

2014
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Publications de l'Institut Mathématique (Beograd)
*

. , F k are the only

doi:10.2298/pim1409101s
fatcat:3q6ammfzq5a5xaom5nkvri76cq
*subdirectly**irreducible*members in it. 2010 Mathematics Subject Classification: Primary 16Y60, 08B05; Secondary 20M07. ... Now, to determine*subdirectly**irreducible*members of DFSR. Lemma 2.1. Let R be a ring in DFSR. If R is*subdirectly**irreducible*, then R is a finite field. ... There are finitely many*subdirectly**irreducible*members in DFSR. ...##
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Page 3766 of Mathematical Reviews Vol. , Issue 86h
[page]

1986
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Mathematical Reviews
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First, we present a characterization of finite

*subdirectly**irreducible*definite*automata*. ... (H-SZEG) On 1;-products of*commutative**automata*. Acta Cybernet. 7 (1985), no. 1, 55-59. ...##
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Page 7277 of Mathematical Reviews Vol. , Issue 2004i
[page]

2004
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Mathematical Reviews
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By characterizing the

*subdirectly**irreducible*members of this class, it is proved that every*commutative*asyn- chronous automaton can be embedded isomorphically into a quasi-direct power of a suitable ... Summary: “The class of the*commutative*asynchronous*automata*are investigated here. ...##
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Page 2219 of Mathematical Reviews Vol. , Issue 93d
[page]

1993
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Mathematical Reviews
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We deal with several of their elementary properties and we characterize the finite

*subdirectly**irreducible*... Summary: “We introduce the notion of (¢; m,)-*commutative*au- tomata, a common generalization of the notions of*commutative*and nilpotent*automata*. ...##
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Discriminator varieties of Boolean algebras with residuated operators

1993
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Banach Center Publications
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algebras, provided they are

doi:10.4064/-28-1-239-252
fatcat:r7elenb6mbhvjceomgj7tcchq4
*subdirectly**irreducible*. ... More specifically, we show that all finite r-algebras, all integral ralgebras, all unital r-algebras with finitely many elements below the unit, and all*commutative*residuated monoids are discriminator ... As a result e is necessarily an atom in any*subdirectly**irreducible**commutative*rm-algebra, and hence the variety of all*commutative*rm-algebras is a subvariety of V e . ...##
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Join decompositions of pseudovarieties involving semigroups with commuting idempotents

2002
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Journal of Pure and Applied Algebra
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have

doi:10.1016/s0022-4049(01)00081-0
fatcat:4nutss5yajehlo5z5qi7wrknmy
*subdirectly**irreducible*transition groups. ... By the remarks above, DH ∩ECom is generated by all transition semigroups of H-good*automata*the group*automata*of which have*subdirectly**irreducible*transition groups. ... If H is arborescent then the decomposition ZE(H) = ACom ∨ H holds where ACom denotes the class of all aperiodic*commutative*semigroups (see [2] ). ...##
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Page 9261 of Mathematical Reviews Vol. , Issue 2002M
[page]

2002
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Mathematical Reviews
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In the case of undirected graphs we show that a graph algebra is syntactic if and only if it is a 0-direct union of

*subdirectly**irreducible*groupoids.” Leonid P. ... We investigate the uniqueness of prime decompositions, as well as the*commuting*of the factors. Inter- connections to languages more general than finite are pointed out. ...##
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Page 540 of Mathematical Reviews Vol. 44, Issue 3
[page]

1972
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Mathematical Reviews
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The author applies his title theorem to prove that a

*commutative*extension (V, o) of a finite (non-trivial) null semigroup S by a cyclic p-group G is*subdirectly**irreducible*if and only if (A) @ is isomor ... Math. 17 (1966), 529-547; MR 33 #5768] has shown that every finite,*commutative*, sub- directly*irreducible*semigroup is one of the following: (i) a group (possibly with zero); (ii) a nilpotent’ semigroup ...
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