On a Pair of (σ, τ)-derivations of Semiprime Γ-rings

Let M be a 2-torsion free G-ring satisfying an assumption and let s,t be centralizing epimorphisms on M. Let f and g be (s, t)-derivations on M such that f(x)αx + xαg(x) = 0 for all xÎM, αÎG. Then we prove that f(u)β[x, y]α = g(u)β[x, y]α = 0 for all x, y, uÎM, α,βÎG and f, g map M into its center.Keywords. Epimorphism; Commuting; Map; Centralizing map; α-derivation; (α, β)-derivation; Prime Gamma-ring; Semiprime Gamma-ring© 2011 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved.doi:10.3329/jsr.v3i3.7659 J. Sci. Res. 3 (3), 525-534 (2011)

Resolving factor maps for shifts of finite type with equal entropy

We sharpen a result of Boyle, Marcus and Trow as follows. An aperiodic shift of finite type ΣAfactors onto another ΣBwith equal entropy by a 1-to-l almost everywhere right-closing map if and only if (1) the dimension group for ΣBis a quotient of that for ΣA; and (2) ΣAand ΣBsatisfy the trivial periodic point condition for existence of a shift-commuting map from ΣAto ΣB.