How to use algebras in a sentence

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Sentence Examples Jordan algebras are called after the German physicist and mathematician Pascual Jordan. His mathematical publications started in 1964 with a series of papers on topological algebras, measure algebras and Banach algebras. Even for propositional logics, models of such systems are usually algebras, e.g., Boolean or Heyting algebras, and as such they are categories. The theorem states that all central division algebras over algebraic number fields are cyclic algebras. In 1984 Jones discovered an astonishing relationship between von Neumann algebras and geometric topology. Malcev also studied Lie groups and topological algebras, producing a synthesis of algebra and mathematical logic. His main work was on associative algebras, non-associative algebras, and Riemann matrices. His work in algebraic number theory led him to study the quaternions and generalisations such as Clifford algebras. His work allowed computations in groups to be replaced by computations in certain polynomial algebras over the field of p elements. He then extended his father's work on associative algebras and worked on mathematical logic and set theory. Cardinal Algebras presents a study of algebras satisfying certain properties which capture the arithmetic of cardinal numbers. In 1941 he received the degree of Doctor of Science for a dissertation Structure of isomorphic representable infinite algebras and groups. Malcev also created a synthesis of the theory of algebras and of algorithms called constructive algebras. He also published results on algebras which were fundamental in the study of algebraic number fields. He also made very substantial contributions to nonassociative algebras, in particular Lie algebras and Jordan algebras. On the web, there are pages on counterexamples in functional analysis, Clifford algebras, and mathematical programming. In 1943 he proved the Gelfand Naimark theorem on self-adjoint algebras of operators in Hilbert space. Topology, cohomology, Lie algebras, and knot theory have all become valuable items in the physicist's tool chest. Two methods of studying the invertibility of operators belonging to the above-mentioned algebras are described. Attempts to create an analogous structure theory for alternative algebras were begun long ago. Show More Sentences Another general algebraic notion which applies to Boolean algebras is the notion of a free algebra. Wedderburn made important advances in the theory of rings, algebras and matrix theory. He had been responsible for major advances in the theory of finite dimensional algebras and was the discoverer of modular representation theory. It completes the formation of the theory of free associative algebras and related classes of rings as an independent domain of ring theory. In 1923 he published important work on real and complex algebras of low dimension. One of the main problems has been and remains the classification of these algebras as intrinsic algebraic and topological objects. This made him a leading light in the rarefied strata of functional analysis, function algebras, field theory and quantization. A congruence permutable variety is a variety all of whose algebras are congruence permutable. He presented a new foundation for and extended the arithmetic of semi-simple algebras over the rational number field. In 1927 he also made notable contributions in hypercomplex numbers, primarily the expansion of the theory of associative ring algebras. Both the decidability results and undecidablity results extend in various ways to Boolean algebras in extensions of first-order logic. We will cover the following subjects. First some algebraic aspects of the theory, concerned with Hecke algebras and their intertwiners. In 1870 Peirce published, at his own expense, Linear Associative Algebra a classification of all complex associative algebras of dimension less than seven. He studied algebras and published papers on trigonometrical series. They relate Boolean algebras to general topology and to the theory of rings and ideals, and include what is called Stone-tech compactification today. In Undecidable theories Tarski showed that group theory, lattices, abstract projective geometry, closure algebras and others mathematical systems are undecidable. Staff expertise in research covers a broad range of mathematics, including operator algebras, solid and fluid mechanics, and quantum mechanics. We extend to the category of crossed modules of Leibniz algebras the notion of biderivation via the action of a Leibniz algebra. Unipotent and nilpotent classes in simple algebraic groups and lie algebras. Section 4 is dedicated to nilpotent Lie algebras and specially to filiform Lie algebras. Show More Sentences Two introductory chapters give background on Cartan geometries, and semisimple Lie algebras and their representations. The Laplace-Beltrami operator is treated only summarily, there is no spectral theory, and the structure theory of Lie algebras is not discussed. These algebras provide a semantics for classical and intuitionistic logic respectively. It is now one of the most active areas of algebras, interacting with, for instance, algebraic geometry, the theory of Lie algebras which appear also in physics, finite groups, quantum groups and also algebraic topology. This algorithm is based on combinatorial techniques which have been developed for dealing with modular representations of symmetric groups, and more generally with representation of Hecke algebras of type A at roots of unity. What is the representation theory of algebras? We also give a way to adapt the construction of classical bases of Lie algebras to superalgebras and dereive consequences on modules and characters. These two processes are inverses of one another, and show that the theory of Boolean algebras and of rings with identity in which every element is idempotent are definitionally equivalent. Tarski's cylindric algebras constitute a particular abstract formulation of first order logic in terms of diagonal relations coding equality and substitution relations encoding variables. Boolean algebra is the algebra of two-valued logic with only sentential connectives, or equivalently of algebras of sets under union and complementation. Noncommutative analogues of classical operations on symmetric functions are investigated, and applied to the description of idempotents and nilpotents in descent algebras. The theory of finite and infinite words with explicit termination is commonly used to give denotational semantics for algebras of sequential processes. It is shown that antidomain semirings are more expressive than test semirings and that Kleene algebras with domain are more expressive than Kleene algebras with tests. On classes of ordered algebras and quasiorder distributivity. Problem 37. A semidirect sum of Lie algebras is a Lie algebra. We prove that assosymmetric algebras under Jordan product are Lie triple. On the index of parabolic subalgebras of semisimple Lie algebras. Torsors, reductive group schemes and extended affine lie algebras. Examples from Classical Literature An introductory chapter reviews elements of differential calculus over commutative algebras. Find more words! 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Words that rhyme with algebras What is the adverb for algebras? What is the adjective for algebras? What is the noun for algebras? Use our Sentence Generator Nearby Words algebraists algebraically algebraical algebraic algebra Algarve Algeciras Alger Algeria Algerian Algerians Algerine 8-letter Words Starting With a al alg alge algeb algebr algebra