CENTRAL SEPARABLE ALGEBRAS OVER LOCAL-GLOBAL RINGS II

Separable Algebras over Commutative Rings

Introduction. The main objects of study in this paper are the commutative separable algebras over a commutative ring. Noncommutative separable algebras have been studied in [2]. Commutative separable algebras have been studied in [1] and in [2], [6] where the main ideas are based on the classical Galois theory of fields. This paper depends heavily on these three papers and the reader should con...

Multiplication operators on Banach modules over spectrally separable algebras

‎Let $mathcal{A}$ be a commutative Banach algebra and $mathscr{X}$ be a left Banach $mathcal{A}$-module‎. ‎We study the set‎ ‎${rm Dec}_{mathcal{A}}(mathscr{X})$ of all elements in $mathcal{A}$ which induce a decomposable multiplication operator on $mathscr{X}$‎. ‎In the case $mathscr{X}=mathcal{A}$‎, ‎${rm Dec}_{mathcal{A}}(mathcal{A})$ is the well-known Apostol algebra of $mathcal{A}$‎. ‎We s...

Triangulaizability of Algebras Over Division Rings

Residually Reducible Representations of Algebras over Local Artinian Rings

In this paper we generalize a result of Urban on the structure of residually reducible representations on local Artinian rings from the case that the semi-simplification of the residual representation splits into 2 absolutely irreducible representations to the case where it splits into m ≥ 2 absolutely irreducible representations.

Trace forms of central simple algebras over a local field or a global field

Introduction: Let A be a central simple algebra over a field k of characteristic different from 2. The quadratic form x ∈ A 7→ TrdA(x ) ∈ k is called the trace form of A, and is denoted by TA. This trace form has been studied by many authors (cf.[L], [LM], [Ti] et [Se], Annexe §5 for example). In particular, these classical invariants are well-known (loc.cit.). In [B], we have determined a diag...