Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Embedding properties of endomorphism semigroups   Denote by PSelf(X) (resp., Self(X)) the partial (resp., full) transformation
monoid over a set X, and by Sub(V) (resp., End(V)) the collection of all
subspaces (resp., endomorphisms) of a vector space V. We prove various results
that imply the following: (1) If X has at least two elements, then Self(X) has
a semigroup embedding into the dual of Self(Y) iff card(Y) >= 2^card(X). In
particular, if X has at least two elements, then there exists no semigroup
embedding from Self(X) into the dual of PSelf(X). (2) If V is
infinite-dimensional, then there are no embedding from (Sub(V),+) into
(Sub(V),\cap) and no semigroup embedding from End(V) into its dual. (3) Let F
be an algebra freely generated by an infinite subset X. If F has less than
2^card(X) operations, then End(F) has no semigroup embedding into its dual. The
cardinality bound 2^card(X) is optimal. (4) Let F be a free left module over a
left aleph one - noetherian ring (i.e., a ring without strictly increasing
chains, of length aleph one, of left ideals). Then End(F) has no semigroup
embedding into its dual. (1) and (2) above solve questions proposed by B. M.
Schein and G. M. Bergman. We also formalize our results in the settings of
algebras endowed with a notion of independence (in particular independence
algebras).

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The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics