ISSN:
1432-0622
Keywords:
p-adic integers
;
Hexagonal tilings
;
Isomorphism
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
,
Mathematics
,
Technology
Notes:
Abstract The primary goal of this paper is to prove that a ring defined by L. Gibson and D. Lucas is isomorphic to the ring of 7-adic integers. The ring, denoted byR 2, arises naturally as an algebraic structure associated with a hexagonal lattice. The elements ofR 2 consist of all infinite sequences in ℤ/(7). The addition and multiplication operations are given in terms of remainder and carries tables. The Generalized Balanced Ternary, denoted byG, is the subring ofR 2 consisting of all the finite sequences ofR 2. IfI k ′ is the ideal ofG consisting of all those sequences whose firstk digits are zero, then the second goal of the paper is to show that the inverse limit ofG/I k ′ is also isomorphic to the 7-adic integers.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01810571
