Open Access$\omega$-Euclidean domain and Laurent series
Author(s) -
Oleh Romaniv,
A. V. Sagan
Publication year - 2016
Publication title -
karpatsʹkì matematičnì publìkacìï
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.