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On countably generated locally $\mathfrak M$-algebras
Yu. M. Ryabukhin
Abstract:
We show how to construct countably generated locally nilpotent groups, rings, and algebras, locally finite groups, rings, and algebras over a finite field, and other countably generated universal algebras possessing certain properties locally. The construction possesses a property close to universality. For example, with each function
$f\colon N\to N$ defined on the natural numbers
$N$ and assuming values in
$N$ there is associated a countably generated locally nilpotent algebra
$\mathscr L(f)$. If
$f$ is an unbounded increasing function, then any countably generated or finitely generated locally nilpotent algebra
$R$ is a homomorphic image of
$\mathscr L(f)$. On the other hand, if
$f$ and
$g$ are any two increasing functions, then
$\mathscr L(f)$ and
$\mathscr L(g)$ are isomorphic if and only if
$f$ and
$g$ agree.
Bibliography: 3 titles.
UDC:
519.48
MSC: 05A15,
08A25 Received: 05.09.1975