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

1983 Mathematical Reviews  
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 [page]

2000 Mathematical Reviews  
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 Mathematical Reviews  
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 Mathematical Reviews  
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 Mathematical Reviews  
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

Yong Shao, Miaomiao Ren, Sinisa Crvenkovic, Melanija Mitrovic
2015 Publications de l'Institut Mathématique (Beograd)  
. , 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 [page]

1982 Mathematical Reviews  
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

Yong Shao, Sinisa Crvenkovic, Melanija Mitrovic
2014 Publications de l'Institut Mathématique (Beograd)  
. , 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 Mathematical Reviews  
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 [page]

2004 Mathematical Reviews  
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 Mathematical Reviews  
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

Peter Jipsen
1993 Banach Center Publications  
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

K. Auinger
2002 Journal of Pure and Applied Algebra  
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 Mathematical Reviews  
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 Mathematical Reviews  
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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