# Construction of a Cyclic Extension of Degree p{sup 2} for a Complete Field

## Abstract

The aim of the paper is to construct an embedding of a given cyclic extension of degree p of a complete discrete valuation field of characteristic 0 with an arbitrary residue field of characteristic p > 0 into a cyclic extension of degree p{sup 2}. The result extends the construction obtained by S. V. Vostokov and I. B. Zhukov in terms of Witt vectors, to a wider interval of values for the ramification jump of the original field extension.

- Authors:

- St. Petersburg State University (Russian Federation)
- St. Petersburg State Electrotechnical University “LETI” (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 22773783

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Mathematical Sciences

- Additional Journal Information:
- Journal Volume: 234; Journal Issue: 2; 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; FIELD EQUATIONS; POLYNOMIALS; VECTORS

### Citation Formats

```
Zhukov, I., E-mail: i.zhukov@spbu.ru, and Lysenko, E., E-mail: lysenkoef@yandex.ru.
```*Construction of a Cyclic Extension of Degree p{sup 2} for a Complete Field*. United States: N. p., 2018.
Web. doi:10.1007/S10958-018-3991-X.

```
Zhukov, I., E-mail: i.zhukov@spbu.ru, & Lysenko, E., E-mail: lysenkoef@yandex.ru.
```*Construction of a Cyclic Extension of Degree p{sup 2} for a Complete Field*. United States. doi:10.1007/S10958-018-3991-X.

```
Zhukov, I., E-mail: i.zhukov@spbu.ru, and Lysenko, E., E-mail: lysenkoef@yandex.ru. Mon .
"Construction of a Cyclic Extension of Degree p{sup 2} for a Complete Field". United States. doi:10.1007/S10958-018-3991-X.
```

```
@article{osti_22773783,
```

title = {Construction of a Cyclic Extension of Degree p{sup 2} for a Complete Field},

author = {Zhukov, I., E-mail: i.zhukov@spbu.ru and Lysenko, E., E-mail: lysenkoef@yandex.ru},

abstractNote = {The aim of the paper is to construct an embedding of a given cyclic extension of degree p of a complete discrete valuation field of characteristic 0 with an arbitrary residue field of characteristic p > 0 into a cyclic extension of degree p{sup 2}. The result extends the construction obtained by S. V. Vostokov and I. B. Zhukov in terms of Witt vectors, to a wider interval of values for the ramification jump of the original field extension.},

doi = {10.1007/S10958-018-3991-X},

journal = {Journal of Mathematical Sciences},

issn = {1072-3374},

number = 2,

volume = 234,

place = {United States},

year = {2018},

month = {10}

}

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