We give a representation theorem for Hilbert algebras by means of ordered sets and characterize the homomorphisms of Hilbert algebras in terms of applications defined between the sets of all irreducible deductive systems of the associated algebras. For this purpose we introduce the notion of order-ideal in a Hilbert algebra and we prove a separation theorem. We also define the concept of semi-h...

3 Topics in Commutative Algebra 2 3.1 Rings and Fields . . . . . . . . . . . . . . . . . . . . . . . . . 2 3.2 Ideals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 3.3 Quotient Rings and Homomorphisms . . . . . . . . . . . . . . 5 3.4 The Characteristic of a Ring . . . . . . . . . . . . . . . . . . . 7 3.5 Polynomial Rings in Several Variables . . . . . . . . . . . . . . 7 3.6...

Let V be an absolutely irreducible representation of a profinite group G over the residue field k of a noetherian local ring O. For local complete O-algebras A with residue field k the representations of G over A that reduce to V over k are given by O-algebra homomorphisms R → A, where R is the universal deformation ring of V . We show this with an explicit construction of R. The ring R is noet...

In the present paper, we study complete and vertical lifts of tensor fields from a smooth manifoldM to its Weil bundle TM defined by a Frobenius Weil algebra A. For a Poisson manifold (M,w), we show that the complete lift w and the vertical lift w of the Poisson tensor w are Poisson tensors on TM and establish their properties. We prove that the complete and the vertical lifts induce homomorphi...

— We investigate the representation theory of the polynomial core T S of the quantum Teichmüller space of a punctured surface S. This is a purely algebraic object, closely related to the combinatorics of the simplicial complex of ideal cell decompositions of S. Our main result is that irreducible finite-dimensional representations of T S are classified, up to finitely many choices, by group hom...

In functional analysis, approximative properties of an object become precise in its ultrapower. We discuss this idea and its consequences for automorphisms of II1 factors. Here are some sample results: (1) an automorphism is approximately inner if and only if its ultrapower is א0-locally inner; (2) the ultrapower of an outer automorphism is always outer; (3) for unital *-homomorphisms from a se...

However it can just as well be considered a fundamental representation theorem of universal algebra, via the connection between the homfunctor of a category and free algebras for the theory represented by that category. This connection is not generally appreciated outside category theoretic circles, which this section endeavors to correct by presenting the relevant concepts from an algebraic pe...

A classical logic exhibits a threefold inner structure comprising an algebra of propositions A, a space of “truth values” V , and a distinguished family of mappings φ from propositions to truth values. Classically A is a Boolean algebra, V = Z2, and the admissible maps φ : A→Z2 are homomorphisms. If one admits a larger set of maps, one obtains an anhomomorphic logic that seems better suited to ...

Based on the structure of Casimir elements associated with general Hopf algebras there are constructed Liouville-Arnold integrable flows related with naturally induced Poisson structures on arbitrary co-algebra and their deformations. Some interesting special cases including the oscillatory Heisenberg-Weil algebra related co-algebra structures and adjoint with them integrable Hamiltonian system...

Given a variety of algebras V, we study categories of algebras in V with a compatible structure of uniform space. The lattice of compatible uniformities of an algebra, Unif A, can be considered a generalization of the lattice of congruences ConA. Mal’cev properties of V influence the structure of Unif A, much as they do that of ConA. The category V[CHUnif] of complete, Hausdorff such algebras i...