5 Abstract Algebra 1 5.1 Binary Operations on Sets . . . . . . . . . . . . . . . . . . . . 1 5.2 Commutative Binary Operations . . . . . . . . . . . . . . . . 2 5.3 Associative Binary Operations . . . . . . . . . . . . . . . . . . 2 5.4 Semigroups . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 5.5 The General Associative Law . . . . . . . . . . . . . . . . . . 4 5.6 Identity elements...

We define a class of algebraic structures for the interpretation of tabular notations common in software requirements documentation and show how to use table algebra homomorphisms to define staged table semantics, translation between different kinds of tables, and table transformation. An important advantage of this approach is that it covers the practically important use of nested headers in a...

7 Abstract Algebra 1 7.1 Binary Operations on Sets . . . . . . . . . . . . . . . . . . . . 1 7.2 Commutative Binary Operations . . . . . . . . . . . . . . . . 2 7.3 Associative Binary Operations . . . . . . . . . . . . . . . . . . 2 7.4 Semigroups . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 7.5 The General Associative Law . . . . . . . . . . . . . . . . . . 4 7.6 Identity elements...

Let A be a graded C∗-algebra. We characterize Kasparov’s K-theory group K̂0(A) in terms of graded ∗-homomorphisms by proving a general converse to the functional calculus theorem for self-adjoint regular operators on graded Hilbert modules. An application to the index theory of elliptic differential operators on smooth closed manifolds and asymptotic morphisms is discussed.

2 Abstract Algebra 24 2.1 Binary Operations on Sets . . . . . . . . . . . . . . . . . . . . 24 2.2 Commutative Binary Operations . . . . . . . . . . . . . . . . 24 2.3 Associative Binary Operations . . . . . . . . . . . . . . . . . . 24 2.4 Semigroups . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.5 The General Associative Law . . . . . . . . . . . . . . . . . . 26 2.6 Identity el...

Starting from a non-standard definition, the descent algebra of the symmetric group is investigated. Homomorphisms into the tensor product of smaller descent algebras are defined. They are used to construct the irreducible representations and to obtain the nilpotency index of the radical.

Abstract Let G be a group and A set equipped with collection of finitary operations. We study cellular automata $$\tau :{A^G} \to {A^G}$$ that preserve the operations induced componentwise from . show τ is an endomorphism if only its local function homomorphism. When entropic (i.e. all are homomorphisms), we establish EndCA( G;A ), consisting such endomorphic automata, isomorphic to direct limi...

The evaluation homomorphisms from the Yangian Y(gln) to the universal enveloping algebra U(gln) allow one to regard the irreducible finite-dimensional representations of gln as Yangian modules. We give necessary and sufficient conditions for irreducibility of tensor products of such evaluation modules. AMS subject classification (2000): 17B37.

This paper surveys, and in some cases generalises, many of the recent results on homomorphisms and the higher Ext groups for q-Schur algebras and for the Hecke algebra of type A. We review various results giving isomorphisms between Ext groups in the two categories, and discuss those cases where explicit results have been determined.

In the first part of this paper, we implement the multiplier algebra of the dual of an algebraic quantum group (A, ∆) (see [13]) as a subset of the space of linear functionals on A. In a second part, we construct the universal corepresentation and use it to prove a bijective corespondence between corepresentations of (A, ∆) and homomorphisms on its dual.