$\omega$-Euclidean domain and Laurent series | Zendy

Oleh Romaniv | Zendy; A. V. Sagan | Zendy

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$\omega$-Euclidean domain and Laurent series

Author(s) -

Oleh Romaniv,

A. V. Sagan

Publication year - 2016

Publication title -

carpathian mathematical publications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.63

H-Index - 4

eISSN - 2313-0210

pISSN - 2075-9827

DOI - 10.15330/cmp.8.1.158-162

Subject(s) - euclidean domain , laurent series , mathematics , domain (mathematical analysis) , ring (chemistry) , euclidean geometry , series (stratigraphy) , commutative ring , euclidean algorithm , laurent polynomial , idempotence , omega , pure mathematics , euclidean distance , euclidean space , commutative property , combinatorics , algebra over a field , euclidean distance matrix , mathematical analysis , geometry , paleontology , chemistry , physics , organic chemistry , quantum mechanics , biology

It is proved that a commutative domain $R$ is $\omega$-Euclidean if and only if the ring of formal Laurent series over $R$ is $\omega$-Euclidean domain. It is also proved that every singular matrice over ring of formal Laurent series $R_{X}$ are products of idempotent matrices if $R$ is $\omega$-Euclidean domain.

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