Similarly, the subfields of a given field form an algebraic system with the operations and where A B means the subfield generated by the subfields A and B . Other examples of such algebraic systems arise when we consider the set of all subspaces of a given vector space or the set of all...
Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the ...
Furthermore, there are important algebraic systems which give rise to non-modular, Birkhoff lattices. Thus, since every exchange lattice (Mac Lane [4]) is a Birkhoff lattice, the systems which satisfy Mac Lane's exchange axiom form lattices of the type in question. In this paper we shall ...
The importance of equational axioms emerged initially with the axiomatic approach to Boolean algebras, groups, and rings, and later in lattices. This unique research monograph systematically presents minimal equational axiom-systems for various lattice-related algebras, regardless of whether they are given...
Elementary Algebraic Structures 2.1.3 Lattice (I) A lattice is a set equipped with an order relation ≤ in which every pair (a, b) has an infimum (or greatest lower bound) a∧ b and a supremum (or least upper bound) a∨ b. The dual lattice may be obtained by reversing the order ...
Igoshin, V.I.,On lattices of algebraic systems quasivarieties, Ordered sets and lattices, 5 Saratov (1978), 44–55 (in Russian). MATHMathSciNetGoogle Scholar Kurosh, A.G.,Group Theory, Nauka, Moscow (1967) (in Russian). Google Scholar ...
Mathematics - Dynamical SystemsMathematics - Group TheoryWe prove an operator algebraic superrigidity statement for homomorphisms of irreducible lattices, and also their commensurators, in certain higher-rank groups into unitary groups of finite factors. This extends the authors' previous work regarding ...
Wille, R.: Tensor products of complete lattices as closure systems. Contributions to General Algebra 7, 381–386 (1991) About this Chapter Title Algebraicity and the Tensor Product of Concept Lattices Book Title Formal Concept Analysis Book Subtitle 12th International Conference, ICFCA 2014, Cl...
We show that, making use of multiplicative lattices and idempotent endomorphisms of an algebraic structure AA, it is possible to derive several notions concerning AA in a natural way. The multiplicative lattice necessary here is the complete lattice of congruences of AA with multiplication given by...
D. Anosov, On homomorphisms of many-sorted algebraic systems in connection with cryptographic applications, Discrete Math. Appl. 17(4) (2007), 331–347. [2] B. H. Arnold, Distributive lattices with a third operation defined, Pacific J. Math. 1 (1951), 33–41. [3] A. Avron, The ...