The Embedding Theorem for Cantor Varieties |
| |
Authors: | L V Shabunin |
| |
Institution: | (1) Moskovskii Prospekt 54-28, Cheboksari, 428017 |
| |
Abstract: | Let m and n be fixed integers, with 1 m < n. A Cantor variety C
m,n is a variety of algebras with m
n-ary and n
m-ary basic operations which is defined in a signature ={g1,...,gm,f1,...,fn} by the identities fig1x1,...,xn),...,gmx1,...,xn) = xi, i=1,...,n, gjf1x1,...,xm),...,fnx1,...,xm)) = xj, j=1,...,m. We prove the following: (a) every partial C
m,n-algebra A is isomorphically embeddable in the algebra G= A; S(A) of C
m,n; (b) for every finitely presented algebra G= A; S in C
m,n, the word problem is decidable; (c) for finitely presented algebras in C
m, the occurrence problem is decidable; (d) C
m,n has a hereditarily undecidable elementary theory. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|