IJPAM: Volume 65, No. 1 (2010)

ON FINITENESS CONDITIONS FOR $S$, $\rho$ AND $S/\rho$

Basri Çaliskan
Karaisali Vocational School
Çukurova University
Adana, 01770, TURKEY
e-mail: [email protected]


Abstract.Let $S$ be a semigroup and let $\rho$ be a congruence on $S$. We consider $%
\rho $ as a subsemigroup of the direct product $S\times S$. Then we prove that $\rho$ is periodic, locally finite and residually finite if and only if $S$ is periodic, locally finite and residually finite, respectively. Moreover, $\rho$ has a solvable word problem if and only if $S$ has a solvable word problem.

Received: July 11, 2009

AMS Subject Classification: 20M05

Key Words and Phrases: congruence, periodicity, local finiteness, residual finiteness, word problem

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 65
Issue: 1