It doesn't have multiplicative inverses; what's the inverse of (0, 0, 1, 1, ..,. )? (make the rest of the elements 1). On Tue, Jan 31, 2017 at 5:05 PM, David Wilson <davidwwilson@comcast.net> wrote:
Consider the set S of sequences where the nth element is a residue of the nth prime. Natural elementwise addition and multiplication operations can be defined on S. With respect to these operations, S has unique additive and multiplicative identities (0 and 1), as well as additive and multiplicative inverses. S also has a subset isomorphic to the integer, where integer k corresponds to the sequence whose nth element is k modulo the nth prime. Not being a number theorist, I was wondering about the algebraic structure of this set.
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