This paper is a contribution to the theory of functor slices of J. Sichler and V. Trnková. For every ordinal α we introduce a basket Eα, prove that every essentially algebraic category of height α is a slice of Eα, characterize small slices of Eα and give a common generalization of known results about slices of the algebraic basket A.

We study algebraic properties of categories of Merotopic, Nearness, and Filter Algebras. We show that the category of filter torsion free abelian groups is an epireflective subcategory of the category of filter abelian groups. The forgetful functor from the category of filter rings to filter monoids is essentially algebraic and the forgetful functor from the category of filter groups to the cat...

we study algebraic properties of categories of merotopic, nearness, and filter algebras. we show that the category of filter torsion free abelian groups is an epireflective subcategory of the category of filter abelian groups. the forgetful functor from the category of filter rings to filter monoids is essentially algebraic and the forgetful functor from the category of filter groups to the cat...

More than two decades ago, Peter Freyd introduced essentially algebraic specifications, a well-behaved generalization of algebraic specifications, allowing for equational partiality. These essentially algebraic specifications turn out to have a number of very interesting applications in computer science. In this paper, we present a deduction system for essentially algebraic specifications that ...

We associate to an algebraic quantum group a C *-algebraic quantum group and show that this C *-algebraic quantum group essentially satisfies an upcoming definition of Masuda, Nakagami & Woronowicz.

Let be a commutative ring with 1 and left unitary . In this paper, the generalizations for notions of compressible module retractable are given. An is termed to semi-essentially if can embedded in every non-zero semi-essential submodules. module, submodule an Some their advantages characterizations examples We also study relation between these classes some other modules.