# Semirings of Continuous (0,∞]-Valued Functions

## Abstract

The semiring C{sup ∞}(X) of all continuous functions on an arbitrary topological space X with values in the topological semiring (0,∞] is studied. General properties of semirings C{sup ∞}(X) are considered. Properties of lattices of ideals and congruences of semirings C{sup ∞}(X) over the P-spaces X, the F-spaces X, and the finite discrete spaces are proved.

- Authors:

- Vyatka State University (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 22773914

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Mathematical Sciences

- Additional Journal Information:
- Journal Volume: 233; Journal Issue: 1; Other Information: Copyright (c) 2018 Springer Science+Business Media, LLC, part of Springer Nature; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1072-3374

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; FUNCTIONS; MATHEMATICAL SPACE; TOPOLOGY

### Citation Formats

```
Vechtomov, E. M., E-mail: vecht@mail.ru, and Shalaginova, N. V., E-mail: korshunnv@mail.ru.
```*Semirings of Continuous (0,∞]-Valued Functions*. United States: N. p., 2018.
Web. doi:10.1007/S10958-018-3923-9.

```
Vechtomov, E. M., E-mail: vecht@mail.ru, & Shalaginova, N. V., E-mail: korshunnv@mail.ru.
```*Semirings of Continuous (0,∞]-Valued Functions*. United States. doi:10.1007/S10958-018-3923-9.

```
Vechtomov, E. M., E-mail: vecht@mail.ru, and Shalaginova, N. V., E-mail: korshunnv@mail.ru. Wed .
"Semirings of Continuous (0,∞]-Valued Functions". United States. doi:10.1007/S10958-018-3923-9.
```

```
@article{osti_22773914,
```

title = {Semirings of Continuous (0,∞]-Valued Functions},

author = {Vechtomov, E. M., E-mail: vecht@mail.ru and Shalaginova, N. V., E-mail: korshunnv@mail.ru},

abstractNote = {The semiring C{sup ∞}(X) of all continuous functions on an arbitrary topological space X with values in the topological semiring (0,∞] is studied. General properties of semirings C{sup ∞}(X) are considered. Properties of lattices of ideals and congruences of semirings C{sup ∞}(X) over the P-spaces X, the F-spaces X, and the finite discrete spaces are proved.},

doi = {10.1007/S10958-018-3923-9},

journal = {Journal of Mathematical Sciences},

issn = {1072-3374},

number = 1,

volume = 233,

place = {United States},

year = {2018},

month = {8}

}

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