Timeline for Generic methods to check irreducibility of polynomials in $K[[X,Y]]$

10 events

when toggle format	what		by	license	comment
Apr 3, 2014 at 11:17	history	edited	Jesse Elliott	CC BY-SA 3.0	added 806 characters in body
Mar 5, 2014 at 9:31	comment	added	Jesse Elliott		As a polynomial in $K[[Y]][X]$, the polynomial $X^7+Y^9$ seems likely to be irreducible. (I think $K[[X]][Y]/(X^7+Y^9)$ is probably just the domain $K[[X]][X^{7/9}]$.) If so then by the theorem you mention it would then be irreducible in $K[[X,Y]]$. If you factor the polynomial over $K[[Y]]$ (which is a complete DVR), then you get one power series factor for each polynomial factor with constant coefficient divisible by $Y$.
Dec 30, 2013 at 17:38	comment	added	brunoh		The problem came up because I was looking at the irreducible polynomial in $K[X,Y]$ mentioned in the text of my question and I tried to see if I understood well some analytic geometry considerations ... Nothing else. Thanks again for your reference !
Dec 30, 2013 at 9:50	vote	accept	brunoh
Dec 30, 2013 at 9:46	history	edited	Jesse Elliott	CC BY-SA 3.0	added 58 characters in body
Dec 30, 2013 at 9:43	comment	added	Jesse Elliott		Glad I could share! I'm curious, how did the problem come up?
Dec 30, 2013 at 9:40	history	edited	Jesse Elliott	CC BY-SA 3.0	added 402 characters in body
Dec 30, 2013 at 9:31	vote	accept	brunoh
Dec 30, 2013 at 9:50
Dec 30, 2013 at 9:31	comment	added	brunoh		@Jesse_Elliott thank you very much ! This paper answers clearly all my questions about this ring,
Dec 30, 2013 at 9:02	history	answered	Jesse Elliott	CC BY-SA 3.0