Subject: Re: binl coefs for 2-adic ints Date: Fri, 01 Jun 2001 10:41:37 -0500 From: Clarence Wilkerson To: Don Davis CC: "dmd1@lehigh.edu (Don Davis)" (Don Davis) <"dmd1"@lehigh.edu>, wilker@math.purdue.edu I think that I know part of this. The 2-adic integers or p-adic integers have the property, like the ordinary integers, that certain binomial coefficients are again 2-adic integers, even though apriori the expressions are in the 2-adic rationals. My memory is that one in this case is looking at \alpha taken k at a time, the expressions that would occur in the formal expansion of (1+x)^{\alpha} as coefficients. I'm not sure what happens if you want k here to be a 2-adic integer. My first impression would be that since the ordinary integers are dense in the 2-adic integers and one could try a definition using limits. Some material on binomial rings and the connection to lambda rings is in a old paper of mine in "Communications in Algebra" in the early 80's. Clarence Wilkerson