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Page 2129 of Mathematical Reviews Vol. , Issue 83e
[page]
1983
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. ...
Page 6188 of Mathematical Reviews Vol. , Issue 2000i
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2000
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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. ...
Page 1428 of Mathematical Reviews Vol. 51, Issue 5
[page]
1976
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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). ...
Page 6888 of Mathematical Reviews Vol. , Issue 98K
[page]
1998
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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. ...
Page 3262 of Mathematical Reviews Vol. , Issue 87f
[page]
1987
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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. ...
The semiring variety generated by any finite number of finite fields and distributive lattices
2015
Publications de l'Institut Mathématique (Beograd)
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. , F k are the only 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. ...
doi:10.2298/pim150404026s
fatcat:6h2k3xzfcbhqfkgp2ojrpwani4
Page 2829 of Mathematical Reviews Vol. , Issue 82g
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1982
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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.)” ...
The variety of semirings generated by distributive lattices and finite fields
2014
Publications de l'Institut Mathématique (Beograd)
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. , F k are the only 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. ...
doi:10.2298/pim1409101s
fatcat:3q6ammfzq5a5xaom5nkvri76cq
Page 3766 of Mathematical Reviews Vol. , Issue 86h
[page]
1986
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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. ...
Page 7277 of Mathematical Reviews Vol. , Issue 2004i
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2004
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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. ...
Page 2219 of Mathematical Reviews Vol. , Issue 93d
[page]
1993
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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. ...
Discriminator varieties of Boolean algebras with residuated operators
1993
Banach Center Publications
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algebras, provided they are 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 . ...
doi:10.4064/-28-1-239-252
fatcat:r7elenb6mbhvjceomgj7tcchq4
Join decompositions of pseudovarieties involving semigroups with commuting idempotents
2002
Journal of Pure and Applied Algebra
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have 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] ). ...
doi:10.1016/s0022-4049(01)00081-0
fatcat:4nutss5yajehlo5z5qi7wrknmy
Page 9261 of Mathematical Reviews Vol. , Issue 2002M
[page]
2002
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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. ...
Page 540 of Mathematical Reviews Vol. 44, Issue 3
[page]
1972
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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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