Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Local morphisms and modules with a semilocal endomorphism ring   An associative ring with 1 is said to be semilocal provided it is semisimple
artinian modulo its Jacobson radical, that is, modulo its Jacobson radical it
is isomorphic to a finite product of matrices over division rings.
  Modules with a semilocal endomorphism ring inherit some properties of
semisimple modules. For example, they can be decomposed into a finite direct
sum of indecomposable submodules, such decomposition is not unique but there
are only a finite number of different ones, they cancel from direct sums and
they satisfy the n-th root uniqueness property.
  A ring homomorphism is said to be local if it carries non-units to non-units.
Semilocal rings can be characterized as those rings having a local homomorphism
to a semisimple artinian ring.
  In this paper show that local homomorphisms appear frequently in module
theory. As a consequence it will follow that many interesting classes of
modules, as for example finitely presented modules over semilocal rings, have a
semilocal endomorphism ring.

33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
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The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
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The categories of this paper are: eess
20
The categories of this paper are: acc-phys