Generalized-pure-hereditary radical classes of Abelian groups
Radicals which define factorization systems
A method due to Fay and Walls for associating a factorization system with a radical is examined for associative rings. It is shown that a factorization system results if and only if the radical is strict and supernilpotent. For groups and non-associative rings, no radical defines a factorization system.
Some aspects of radical theory for fully ordered Abelian groups
How to make many-sorted algebras one-sorted
Two notes on radicals of Abelian groups
Epimorphisms of regular rings
Rings on completely decomposable torsion-free Abelian groups
Extension-closure and attainability for varieties of algebras with involution
Ring varieties closed under ideal sums
A note on ring epimorphisms and polynomial identities
Closure rings
We consider rings equipped with a closure operation defined in terms of a collection of commuting idempotents, generalising the idea of a topological closure operation defined on a ring of sets. We establish the basic properties of such rings, consider examples and construction methods, and then concentrate on rings which have a closure operation defined in terms of their lattice of central idempotents.
Rings on certain classes of torsion-free Abelian groups
Directoid groups
We continue the study of directoid groups, directed abelian groups equipped with an extra binary operation which assigns an upper bound to each ordered pair subject to some natural restrictions. The class of all such structures can to some extent be viewed as an equationally defined substitute for the class of (2-torsion-free) directed abelian groups. We explore the relationship between the two associated categories, and some aspects of ideals of directoid groups.
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