Isomorphisms of Semirings of Continuous Nonnegative Functions and the Lattices of Their Subalgebras

Let be the semifield with zero of nonnegative real numbers or the semifield of positive real numbers. The set of all continuous functions with pointwise operations of addition and multiplication of functions defined on an arbitrary topological space forms the semiring By a subalgebra we mean a nonem...

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Bibliographic Details
Published in:Lobachevskii journal of mathematics 2020-09, Vol.41 (9), p.1684-1692
Main Author: Sidorov, V. V.
Format: Article
Language:English
Subjects:
Algebra
Analysis
Continuity (mathematics)
Geometry
Isomorphism
Lattices (mathematics)
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Multiplication
Probability Theory and Stochastic Processes
Real numbers
Rings (mathematics)
Topology
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Summary:Let be the semifield with zero of nonnegative real numbers or the semifield of positive real numbers. The set of all continuous functions with pointwise operations of addition and multiplication of functions defined on an arbitrary topological space forms the semiring By a subalgebra we mean a nonempty subset of such that for any and any For arbitrary topological spaces and we describe isomorphisms of the semirings and and isomorphisms of the lattices of their subalgebras (subalgebras with unity).
ISSN:1995-0802
1818-9962
DOI:10.1134/S1995080220090255