ment
work
H. Stone
algebraic
Boolean Algebras
en
content
algebraic one
set
era
theorem
algebraic rings
special kind
little mention
stones
mention
https://scigraph.springernature.com/explorer/license/
point
book
aspects
part
978-3-642-85822-2
new era
fundamental theorem
Boolean operations
chapter
algebra
There are two aspects to the theory of Boolean algebras; the algebraic and the set-theoretical. A Boolean algebra can be considered as a special kind of algebraic ring, or as a generalization of the set-theoretical notion of a field of sets. Fundamental theorems in both of these directions are due to M. H. STONE, whose papers have opened a new era in the develop ment of this theory. This work treats the set-theoretical aspect, with little mention being made of the algebraic one. The book is composed of two chapters and an appendix. Chapter I is devoted to the study of Boolean algebras from the point of view of finite Boolean operations only; a greater part of its contents can be found in the books of BIRKHOFF [2J and HERMES [1]. Chapter II seems to be the first systematic study of Boolean algebras with infinite Boolean operations. To understand Chapters I and II it suffices only to know fundamental notions from general set theory and set-theoretical topology. No know ledge of lattice theory or of abstract algebra is presumed. Less familiar topological theorems are recalled, and only a few examples use more advanced topological means; but these may be omitted. All theorems in both chapters are given with full proofs.
notion
Birkhoff
ring
false
point of view
https://doi.org/10.1007/978-3-642-85820-8
Boolean algebra
set-theoretical notions
direction
operation
1969-01-01
books
2022-05-10T10:34
field of sets
greater part
book
theory
1969
kind
978-3-642-85820-8
field
view
study
paper
chapter I
appendix
generalization
one
Mathematical Sciences
doi
10.1007/978-3-642-85820-8
dimensions_id
pub.1045547780
Pure Mathematics
Springer Nature
Springer Nature - SN SciGraph project