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010   $a3-319-21200-1
024 7 $a10.1007/978-3-319-21200-5
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035   $a(DE-He213)978-3-319-21200-5
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035   $a(PPN)190518731
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100   $a20150908d2015      u|         0
101 0 $aeng
135   $aur|n|---|||||
181   $ctxt
182   $cc
183   $acr
200 14$aThe equationally-defined commutator $ea study in equational logic and algebra /$fby Janusz Czelakowski
205   $a1st ed. 2015.
210  1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2015.
215   $a1 online resource (297 p.)
300   $aDescription based upon print version of record.
311   $a3-319-21199-4 
320   $aIncludes bibliographical references and indexes.
327   $aIntroduction -- Basic Properties of Quasivarieties -- Commutator Equations and the Equationally Defined Commutator -- Centralization Relations -- Additivity of the Equationally Defined Commutator -- Modularity and Related Topics -- Additivity of the Equationally Defined Commutator and Relatively Congruence-Distributive Dub quasivarieties -- More on Finitely Generated Quasivarieties -- Commutator Laws in Finitely Generated Quasivarieties -- Appendix 1: Algebraic Lattices -- Appendix 2: A Proof of Theorem 3.3.4 for Relatively Congruence-Modular Quasivarieties -- Appendix 3: Inferential Bases for Relatively Congruence-Modular Quasivarieties.
330   $aThis monograph introduces and explores the notions of a commutator equation and the equationally-defined commutator from the perspective of abstract algebraic logic. An account of the commutator operation associated with equational deductive systems is presented, with an emphasis placed on logical aspects of the commutator for equational systems determined by quasivarieties of algebras. The author discusses the general properties of the equationally-defined commutator, various centralization relations for relative congruences, the additivity and correspondence properties of the equationally-defined commutator, and its behavior in finitely generated quasivarieties. Presenting new and original research not yet considered in the mathematical literature, The Equationally-Defined Commutator will be of interest to professional algebraists and logicians, as well as graduate students and other researchers interested in problems of modern algebraic logic.
606   $aGroup theory
606   $aCommutative algebra
606   $aCommutative rings
606   $aAssociative rings
606   $aRings (Algebra)
606   $aGroup Theory and Generalizations$3https://scigraph.springernature.com/ontologies/product-market-codes/M11078
606   $aCommutative Rings and Algebras$3https://scigraph.springernature.com/ontologies/product-market-codes/M11043
606   $aAssociative Rings and Algebras$3https://scigraph.springernature.com/ontologies/product-market-codes/M11027
615  0$aGroup theory.
615  0$aCommutative algebra.
615  0$aCommutative rings.
615  0$aAssociative rings.
615  0$aRings (Algebra)
615 14$aGroup Theory and Generalizations.
615 24$aCommutative Rings and Algebras.
615 24$aAssociative Rings and Algebras.
676   $a510
700   $aCzelakowski$b Janusz$4aut$4http://id.loc.gov/vocabulary/relators/aut$0755628
906   $aBOOK
912   $a9910300242903321
996   $aThe Equationally-Defined Commutator$92502870
997   $aUNINA