JP Journal of Algebra, Number Theory and Applications
Volume 1, Issue 3, Pages 225 - 233
(December 2001)
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HOMOMORPHISMS BETWEEN MATRIX MULTIPLICATIVE SEMIGROUPS
Xian Zhang (P. R. China) and Chong-Guang Cao (P. R. China)
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Abstract: Let
Mn
be the multiplicative semigroup of n´n
matrices
over a field F
and Dn
be
a subsemigroup which satisfies Gn
=
{aEij|a Î
F, 1 £
i, j £
n} Í
D
n Í
Mn, where aEij is the matrix with a
in the (i, j ) position and
0 elsewhere. We characterize those
homomorphisms f from Dn
to
Mn. Thereby, we determine
the form of those homomorphisms from Dn
to
Mn
which preserve the spectrum (see [Lin. Alg.
Appl. 212/312 (1994), 339-351]), preserve the
rank, preserve the trace, or are spectrum non-
increasing. |
Keywords and phrases: homomorphism,
multiplicative semigroup, spectrum, trace, rank, spectrum
non-increasing. |
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