An isomorphism theorem between the 7-adic integers and a ring associated with a hexagonal lattice

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 byR₂, arises naturally as an algebraic structure associated with a hexagonal lattice. The elements ofR₂ consist of all infinite sequences in /(7). The addition and multiplication operations are given in terms of remainder and carries tables. The Generalized Balanced Ternary, denoted byG, is the subring ofR₂ consisting of all the finite sequences ofR₂. 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.