.

0 (hodnocen0 x )

BK

Berlin : Heldermann, 1990

568 s. : il.

ISBN 3-88538-008-0 (váz.)

Sigma series in pure mathematics ; [vol.] 8

Obsahuje: obsah, úvod, rejstřík

Bibliografie: s. 467 - 555

Algebra - učebnice vysokošk.

Pologrupy - okruhy - úvod,teorie,aplikace - algebra - výklady odborné

000088247

Contents // Introduction...ix // Chapter I // T. Evans: Varieties of loops and quasigroups...1 // 1.1 Universal algebraic preliminaries...1 // 1.2 Free loops and quasigroups...7 // 1.3 Decision problems and the structure of finitely presented loops...11 // 1.4 Classifying loop identities and loop varieties...16 // 1.5 Quasigroup varieties and combinatorics...22 // Chapter II // O. Chein: Examples and methods of construction...27 // II. 1 Introduction...27 // 11.2 Terminology...28 // 11.3 Extensions...35 // 11.4 Other constructions using cartesian products...43 // 11.5 botopy...51 // 11.6 New operations on algebraic systems...58 // II. 7 Miscellaneous algebraic constructions...63 // 11.8 Constructions arising from geometry... 74 // 11.9 Constructions based on designs...83 // II. 10 Summary...90 // Chapter III // J. D. H. Smith: Centrality...95 // III. 1 Introduction... 95 // 111.2 Equasigroups and their congruences...95 // 111.3 Central congruences...98 // 111.4 Central isotopy...102 // 111.5 3-quasigroups...105 // 111.6 Stability conguences... 110 // vi // Contents // Chapter IV // L. Bénéteau: Commutative Moufang loops and related groupoids...115 // IV. 1 Preliminaries...115 // IV. 2 Basic facts about central nilpotence and first consequences...122 // rV.3 Free objects, related groups, and open problems...128 // Chapter V // L. Bénéteau: Cubic hypersurface quasigroups...143 // V. l Definitions and structure theorems...143 // V. 2 Geometrical motivations...146 // Chapter VI

// M. Deza, G. Sabidussi: Combinatorial structures arising from commutative // Moufang loops...151 // VI. 1 Introduction... 151 // VI.2 Matroidal background...153 // VI.3 Hall systems as perfect matroid designs...154 // VI.4 Erigibility... 156 // VI. 5 Dimensions...159 // Chapter VII // E. G. Goodaire, M. J. Kallaher: Systems with two binary operations, // and their planes...161 // VILI Introduction and historical background...161 // VII. 2 Ternary rings and their planes...162 // VII.3 Quasifields...169 // VII.4 Semifields...176 // VII.5 Derivability...180 // VII.6 Construction of cartesian groups...183 // VII.7 Neofields...186 // VII. 8 Loop rings...189 // Chapter VIII // A. Barlotti: Geometry of quasigroups...197 // VIII. l Introduction...197 // VIII.2 Staudt’s point of view...197 // VIII.3  -transitive and ( -transitive permutation groups...201 // VIII.4 Klein’s point of view in web geometry...202 // VI // Contents // Chapter IV // L. Bénéteau: Commutative Moufang loops and related groupoids...115 // IV.1 Preliminaries...115 // IV.2 Basic facts about central nilpotence and first consequences...122 // IV. 3 Free objects, related groups, and open problems...128 // Chapter V // L. Bénéteau: Cubic hypersurface quasigroups...143 // V. l Definitions and structure theorems...143 // V. 2 Geometrical motivations...146 // Chapter VI // M. Deza, G. Sabidussi: Combinatorial structures arising from commutative // Moufang loops...151 // VI. 1 Introduction... 151 // VI.2 Matroidal

background...153 // VI.3 Hall systems as perfect matroid designs...154 // VI.4 Erigibility...156 // VI. 5 Dimensions...159 // Chapter VII // E. G. Goodaire, M. J. Kallaher: Systems with two binary operations, // and their planes... 161 // VILI Introduction and historical background...161 // VII. 2 Ternary rings and their planes...162 // VII.3 Quasifields...169 // VII.4 Semifields... 176 // VII.5 Derivability... 180 // VII.6 Construction of cartesian groups...183 // VII.7 Neofields...186 // VII. 8 Loop rings...189 // Chapter VIII // A. Barlotti: Geometry of quasigroups...197 // VIII. l Introduction...197 // VIII.2 Staudt’s point of view...197 // VIIL3  -transitive and w-transitive permutation groups... 201 // VIII.4 Klein’s point of view in web geometry...202 // Contents // viii // Chapter XII // P. ?. Miheev, L. V. Sabinin: Quasigroups and differential geometry...357 // ??? Smooth universal algebra...359 // XII.2 Canonical affine connections of loopuscular and geoodular structures...366 // XII.3 Reductive and symmetric geoodular spaces...374 // XII.4 s-Spaces... 389 // XII.5 Lie triple algebras...395 // XII.6 Semidirect products of a quasigroup by its transassociants...398 // XII.7 The infinitesimal theory of local analytic loops...405 // XII. 8 Smooth Boi loops...418 // Chapter XIII // P. D. Gerber: LIP loops and quadratic differential equations...431 // XIII. 1 Introduction...431 // XIII.2 Notation and general background...431 // XIII.3 Quadratic systems...435 // XIII.4

First degree groups...437 // XIII. 5 First degree LIP loops...440 // Chapter XIV // F. B. Kalhoff, S. H. G. Prieß-Crampe: Ordered loops and ordered // planar ternary rings...445 // XIV. 1 Some basic facts about ordered loops...446 // XIV.2 Archimedean ordering...448 // XIV.3 Chain of convex subloops and orderability of loops...451 // XIV.4 Ordered double loops and ordered planar ternary rings...454 // XIV.5 Archimedean planar ternary rings and double loops...458 // XIV.6 Preorderings and Artin-Schreier characterization in PTRs...461 // XIV.7 Spaces of orderings and Witt rings of planar ternary rings...463 // Bibliography...467 // Subject index // 557