Fundamental Structures of Algebra and Discrete Mathematics
John Wiley & Sons, 16 mars 1994 - 344 pages
Introduces and clarifies the basic theories of 12 structural concepts, offering a fundamental theory of groups, rings and other algebraic structures. Identifies essentials and describes interrelationships between particular theories. Selected classical theorems and results relevant to current research are proved rigorously within the theory of each structure. Throughout the text the reader is frequently prompted to perform integrated exercises of verification and to explore examples.
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affine geometry algebraic closure algebraic closure system axioms belongs bijection binary operation binary relation Boolean lattice called Card cardinal chain Chapter chromatic polynomial closed sets closure operator coincides commutative complement congruence containing convex coset covering graph covering relation cycle cyclic defined denoted disjoint distributive lattice equational equipotent Euclidean example factors field F filter finite set flat formal theory geometric lattice given graph G group G groupoid Helly number homomorphism ideal identity implies inclusion-ordered set injective intersection inverse isomorphic Lemma mathematical matroid maximal median modular monoid morphism multiplicative natural number nonzero normal subgroup Obviously ordered set ordinal function permutation group power set preorder prime Proof Proposition quotient reader real numbers ring root semigroup Show singleton structure sublattice subring subspace surjective Theorem tion topological space topology Tutte polynomial ultrafilter unique universal algebra vector space Verify vertex write zero