Climent, Joan-Josep, Navarro, Pedro R., Tortosa, Leandro
On the arithmetic of the endomorphisms ring End(Zp×Zp2)
Applicable Algebra in Engineering, Communication and Computing. 2011, 22(2): 91-108. doi:10.1007/s00200-011-0138-4
URI: http://hdl.handle.net/10045/34676
DOI: 10.1007/s00200-011-0138-4
ISSN: 0938-1279 (Print)
Abstract: 
For a prime number p, Bergman (Israel J Math 18:257–277, 1974) established that End(Zp×Zp2) is a semilocal ring with p 5 elements that cannot be embedded in matrices over any commutative ring. We identify the elements of End(Zp×Zp2) with elements in a new set, denoted by E p , of matrices of size 2 × 2, whose elements in the first row belong to Zp and the elements in the second row belong to Zp2 ; also, using the arithmetic in Zp and Zp2 , we introduce the arithmetic in that ring and prove that the ring End(Zp×Zp2) is isomorphic to the ring E p . Finally, we present a Diffie-Hellman key interchange protocol using some polynomial functions over E p defined by polynomials in Z[X].
Keywords:Endomorphism, Isomorphism, Noncommutative ring, Additive order, Invertible element, Key exchange protocol
Springer
info:eu-repo/semantics/article