عنوان
پدید آورنده
موضوع
رده
کتابخانه
محل استقرار
INTERNATIONAL STANDARD BOOK NUMBER
(Number (ISBN
9789048152704
(Number (ISBN
9789401592413
NATIONAL BIBLIOGRAPHY NUMBER
Number
b408403
TITLE AND STATEMENT OF RESPONSIBILITY
Title Proper
Power Algebras over Semirings
General Material Designation
[Book]
Other Title Information
With Applications in Mathematics and Computer Science /
First Statement of Responsibility
by Jonathan S. Golan.
.PUBLICATION, DISTRIBUTION, ETC
Place of Publication, Distribution, etc.
Dordrecht :
Name of Publisher, Distributor, etc.
Imprint: Springer,
Date of Publication, Distribution, etc.
1999.
SERIES
Series Title
Mathematics and Its Applications ;
Volume Designation
488
CONTENTS NOTE
Text of Note
Some (hopefully) motivating examples -- 0: Background material -- 1: Powers of a semiring -- 2: Relations with values in a semiring -- 3: Change of base semirings -- 4: Convolutions -- 5: Semiring-valued subsemigroups and submonoids -- 6: Semiring-valued groups -- 7: Semiring-valued submodules and subspaces -- 8: Semiring-valued ideals in semirings and rings -- References.
0
SUMMARY OR ABSTRACT
Text of Note
This monograph is a continuation of several themes presented in my previous books [146, 149]. In those volumes, I was concerned primarily with the properties of semirings. Here, the objects of investigation are sets of the form RA, where R is a semiring and A is a set having a certain structure. The problem is one of translating that structure to RA in some "natural" way. As such, it tries to find a unified way of dealing with diverse topics in mathematics and theoretical com puter science as formal language theory, the theory of fuzzy algebraic structures, models of optimal control, and many others. Another special case is the creation of "idempotent analysis" and similar work in optimization theory. Unlike the case of the previous work, which rested on a fairly established mathematical foundation, the approach here is much more tentative and docimastic. This is an introduction to, not a definitative presentation of, an area of mathematics still very much in the making. The basic philosphical problem lurking in the background is one stated suc cinctly by Hahle and Sostak [185]: ". . . to what extent basic fields of mathematics like algebra and topology are dependent on the underlying set theory?" The conflicting definitions proposed by various researchers in search of a resolution to this conundrum show just how difficult this problem is to see in a proper light.
OTHER EDITION IN ANOTHER MEDIUM
International Standard Book Number
9789048152704
PIECE
Title
Springer eBooks
TOPICAL NAME USED AS SUBJECT
Algebra.
Computational complexity.
Logic, Symbolic and mathematical.
Mathematics.
PERSONAL NAME - PRIMARY RESPONSIBILITY
Golan, Jonathan S.
CORPORATE BODY NAME - ALTERNATIVE RESPONSIBILITY
SpringerLink (Online service)
ORIGINATING SOURCE
Date of Transaction
20190307161000.0
ELECTRONIC LOCATION AND ACCESS
Electronic name
مطالعه متن کتاب [Book]
Y
