Banaschewski’s theorem for generalized <Emphasis Type="Italic">MV</Emphasis>-algebras

A generalized MV-algebra A is called representable if it is a subdirect product of linearly ordered generalized MV-algebras. Let S be the system of all congruence relations ϱ on A such that the quotient algebra A/ϱ is representable. In the present paper we prove that the system S has a least element. This work was supported by Science and Technology Assistance Agency under Contract No AVPT-51-032002. The work has been partially supported by the Slovak Academy of Sciences via the project Center of Excellence-Physics of Information (grant I/2/2005).