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008 170212s2015 gw | s |||| 0|eng d
020 _a9783319212005
_9978-3-319-21200-5
024 7 _a10.1007/978-3-319-21200-5
_2doi
035 _ato000560433
040 _aSpringer
_cSpringer
_dRU-ToGU
050 4 _aQA174-183
072 7 _aPBG
_2bicssc
072 7 _aMAT002010
_2bisacsh
082 0 4 _a512.2
_223
100 1 _aCzelakowski, Janusz.
_eauthor.
_9467601
245 1 4 _aThe Equationally-Defined Commutator
_helectronic resource
_bA Study in Equational Logic and Algebra /
_cby Janusz Czelakowski.
250 _a1st ed. 2015.
260 _aCham :
_bSpringer International Publishing :
_bImprint: Birkhäuser,
_c2015.
300 _aIX, 292 p. 3 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
505 0 _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.
520 _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.
650 0 _amathematics.
_9566183
650 0 _aAssociative rings.
_9205882
650 0 _aRings (Algebra).
_9460211
650 0 _aCommutative algebra.
_9466051
650 0 _aCommutative rings.
_9466052
650 0 _aGroup theory.
_9303360
650 1 4 _aMathematics.
_9566184
650 2 4 _aGroup Theory and Generalizations.
_9303362
650 2 4 _aCommutative Rings and Algebras.
_9303210
650 2 4 _aAssociative Rings and Algebras.
_9306398
710 2 _aSpringerLink (Online service)
_9143950
773 0 _tSpringer eBooks
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-319-21200-5
912 _aZDB-2-SMA
999 _c415256