7,785 research outputs found
Krull-Schmidt decompositions for thick subcategories
Following Krause \cite{Kr}, we prove Krull-Schmidt type decomposition
theorems for thick subcategories of various triangulated categories including
the derived categories of rings, Noetherian stable homotopy categories, stable
module categories over Hopf algebras, and the stable homotopy category of
spectra. In all these categories, it is shown that the thick ideals of small
objects decompose uniquely into indecomposable thick ideals. We also discuss
some consequences of these decomposition results. In particular, it is shown
that all these decompositions respect K-theory.Comment: Added more references, fixed some typos, to appear in Journal of Pure
and Applied Algebra, 22 pages, 1 figur
What is special about the divisors of 24?
What is an interesting number theoretic or a combinatorial characterization
of the divisors of 24 amongst all positive integers? In this paper I will
provide one characterization in terms of modular multiplication tables. This
idea evolved interestingly from a question raised by a student in my elementary
number theory class. I will give the characterization and then provide 5 proofs
using various techniques: Chinese remainder theorem, structure theory of units,
Dirichlet's theorem on primes in an arithmetic progression, Bertrand-Chebyshev
theorem, and results of Erdos and Ramanujan on the pi(x) function.Comment: 7 pages, to appear in Math. Ma
- …