8 papers · 1 filter
The factorization system of a radical on a homological category
Dali Zangurashvili
Employing the techniques of transporting a factorization system from one category to another via an adjunction, developed in our earlier papers, a factorization system is related t…
Descent in the dual category of ternary rings
Guram Samsonadze, Dali Zangurashvili
It is shown that, in the variety of ternary rings, the elements of amalgamated free products have unique normal forms, and, moreover, this variety satisfies the strong amalgamation…
Cokernels in the stable category of a left hereditary ring
Dali Zangurashvili
It is proved that if a ring is left hereditary, left perfect and right coherent, then the stable category has cokernels. Moreover, we show that the condition for a ring to be left…
Ideals in BIT speciale varieties
Dali Zangurashvili
Ideals in BIT speciale varieties are characterized. In particular, it is proved that, for any finitary BIT speciale variety, there is a finite set of ideal terms determining ideals…
Right-cancellable protomodular algebras
Dali Zangurashvili
A new protomodular analog of the classical criterion for the existence of a group term in the algebraic theory of a variety of universal algebras is given. To this end, the notion…
Associative Protomodular Algebras
Dali Zangurashvili
The notion of associativity (which differs from the straightforward generalization of the usual associativity given by the move of parentheses in the relevant expression) for opera…