scholarly journals Point stabilisers for the enhanced and exotic nilpotent cones

2011 ◽  
Vol 14 (6) ◽  
Author(s):  
Michael Sun
Keyword(s):  
Finite Field ◽  
Direct Product ◽  
Product Decomposition ◽  
Direct Product Decomposition

AbstractWe give a semi-direct product decomposition of the point stabilisers for the enhanced and exotic nilpotent cones. In particular, we arrive at formulas for the number of points in each orbit over a finite field, which is in accordance with a recent conjecture of Achar and Henderson.

Direct product decomposition of theories of modules

1979 ◽  
Vol 44 (1) ◽  
pp. 77-88 ◽  
Author(s):  
Steven Garavaglia
Keyword(s):  
Direct Product ◽  
Regular Ring ◽  
Decomposition Theorem ◽  
Direct Products ◽  
Product Decomposition ◽  
Von Neumann Regular Ring ◽  
Von Neumann ◽  
Direct Product Decomposition ◽  
Von Neumann Regular ◽  
Complete Theories

This paper is mainly concerned with describing complete theories of modules by decomposing them (up to elementary equivalence) into direct products of simpler modules. In §1, I give a decomposition theorem which works for arbitrary direct product theories T. Given such a T, I define T-indecomposable structures and show that every model of T is elementarily equivalent to a direct product of T-indecomposable models of T. In §2, I show that if R is a commutative ring then every R-module is elementarily equivalent to ΠMM where M ranges over the maximal ideals of R and M is the localization of at M. This is applied to prove that if R is a commutative von Neumann regular ring and TR is the theory of R-modules then the TR-indecomposables are precisely the cyclic modules of the form R/M where M is a maximal ideal. In §3, I use the decomposition established in §2 to characterize the ω1-categorical and ω-stable modules over a countable commutative von Neumann regular ring and the superstable modules over a commutative von Neumann regular ring of arbitrary cardinality. In the process, I also prove several general characterizations of ω-stable and superstable modules; e.g., if R is any countable ring, then an R-moduIe is ω-stable if and only if every R-module elementarily equivalent to it is equationally compact.

A direct product decomposition of QMV algebras

2012 ◽  
Vol 55 (4) ◽  
pp. 841-850
Author(s):  
Xian Lu ◽  
Yun Shang ◽  
RuQian Lu
Keyword(s):  
Direct Product ◽  
Product Decomposition ◽  
Direct Product Decomposition ◽  
Qmv Algebras
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