Indecomposable division algebras

Indecomposable Division Algebras with a Baer Ordering

In this paper we construct Baer ordered indecomposable division algebras of index pn and exponent pm for all primes p and for all n, m, with n > m ≥ 1 (n ≥ 3 if p = 2).

Indecomposable Ideals in Incidence Algebras ⋆

The elements of a finite partial order P can be identified with the maximal indecomposable two-sided ideals of its incidence algebra A, and then for two such ideals, I ≺ J ⇐⇒ IJ 6= 0. This offers one way to recover a poset from its incidence algebra. In the course of proving the above, we classify all of the two-sided ideals of A. In contemporary physical theory, the concept of a “space” or, mo...

INDECOMPOSABLE AND NONCROSSED PRODUCT DIVISION ALGEBRAS OVER FUNCTION FIELDS OF SMOOTH p-ADIC CURVES

We construct indecomposable and noncrossed product division algebras over function fields of smooth curves X over Zp. This is done by defining an index preserving morphism s : Br(K̂(X)) → Br(K(X)) which splits res : Br(K(X)) → Br(K̂(X)), where K̂(X) is the completion of K(X) at the special fiber, and using it to lift indecomposable and noncrossed product division algebras over K̂(X).

Triangulaizability of Algebras Over Division Rings

Indecomposable Representations of Finite-Dimensional Algebras

Let 1c "be a field and A a finite-dimensional 7c-algebra (associative, with 1). AVe consider representations of A as rings of endomorpliisms of finitedimensional 7c-spaces, and thus JL-modules, and we ask for a classification of such representations. More generally, we may consider the following problem: given an abelian category # and simple ( = irreducible) objects F(l),..., B(n) in #, what a...