Categories of Algebraic Systems Vector and Projective Spaces, Semigr
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553 Mario Petrich
Categories of Algebraic Systems Vector and Projective Spaces, Semigroups, Rings and Lattices ETHICS ETH-HB .001@~0~0139017"
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Springer-Verlag Berlin.Heidelberg 9New York 197 6
Author
Mario Petrich Department of Mathematics Pennsylvania State University University Park, P A / U S A
Library of Congress Cataloging in Publication Data
Petrieh, Mario. Categories of algebraic systems. (Lecture motes in mathematics ; 553) Bibliography: p. Includes index. i. Algebra~ Abstract. 2. Categories (Mathematics) I. Title. II. Series: Lecture notes in mathematics
(Berlm)
QA3.LT8
; 553.
no. 553
[QAA62] 510'.8s [512]
76-53511
AMS Subject Classifications (1970): 06A30, 16A12, 20M25, 15A63, 16A28, 50D25, 50D30 ISBN 3-540-07998-X Springer-Verlag Berlin 9 Heidelberg 9 New York ISBN 0-387-07998-X Springer-Verlag New York 9 Heidelberg 9 Berlin This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under w 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to the publisher, the amount of the fee to be determined by agreement with the publisher. 9 by Springer-Verlag Berlin 9 Heidelberg 1976 Printed in Germany Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr.
PREFACE
The leitmotiv
mathematics mentioned
of this monograph
encompassed
in its title.
still lack " status
ometry have been established,
what have we gained, gain,
similar the underlying
and embarass-
what can we do now that we could
so far, is the realization
ideas in these different
area is better developed.
in some " poorer
or failure,
would illustrate
" ones,
e.g.,
" branches
semigroups
it is a small amount of knowledge in its title.
only a familiarity
ble understanding
importantly,
The prerequisite
Its success,
really carry.
for reading
of, or feeling for, some of the
Hence
with general
following
an advanced
interest
an " open mind ".
for a reasona-
graduate
student
in some of these
maturity
of category theory is presuposed.
theory itself, w i t h one exception,
for
this study. The real prere-
minimum degree of " mathematical
No knowledge
spaces.
with a few of these areas suffices
should have no trouble
quisite is a
vs. vector
One can get away with much less,
of the material.
or a research mathematician
surely lead to
inspired by the theory in
how far these relationships
For whom is this monograph written?
about the
system in another
This type of research would
new results
subjects
areas
in one of these areas and deduce the corresponding
of a system in one area if the analogous
areas mentioned
how
are. We are not yet able to
one in another area ", but we are able to pose questions
some " richer
and
of algebra and ge-
one may pose the natural,
are,
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