Epimorphisms onto Derivation Algebras

Center--like subsets in rings with derivations or epimorphisms

We introduce center-like subsets Z*(R,f), Z**(R,f) and Z1(R,f), where R is a ring and f is a map from R to R. For f a derivation or a non-identity epimorphism and R a suitably-chosen prime or semiprime ring, we prove that these sets coincide with the center of R.

NOTES ON EFFECTIVE DESCENT AND PROJECTIVITY IN QUASIVARIETIES OF UNIVERSAL ALGEBRAS Dedicated to Walter Tholen on the occasion of his sixtieth birthday

We present sufficient conditions under which effective descent morphisms in a quasivariety of universal algebras are the same as regular epimorphisms and examples for which they are the same as regular epimorphisms satisfying projectivity. 1. Preliminaries A variety is a full subcategory of the category of structures for a first order (one sorted) language, closed under substructures, products ...

Not all Epimorphisms are Surjective in the Class of Diagonal Cylindric Algebras

Let α be an infinite ordinal. We show that not all epimorphisms are surjective in the class Diα of diagonal cylindric algebras (regarded as a concrete category). It follows that Diα does not have the strong amalgamation property. This answers a question of Pigozzi.

Revised working draft (31 January 2016) EPIMORPHISMS IN VARIETIES OF RESIDUATED STRUCTURES

It is proved that epimorphisms are surjective in a range of varieties of residuated structures, including all varieties of Heyting or Brouwerian algebras of finite depth, and all varieties consisting of Gödel algebras, relative Stone algebras, Sugihara monoids or positive Sugihara monoids. This establishes the infinite deductive Beth definability property for a corresponding range of substructu...

Prime Higher Derivations on Algebras