We construct a structure of a ring with local units on a co-Frobenius coalgebra. We study a special class of co-Frobenius coalgebras whose objects we call symmetric coalgebras. We prove that any semiperfect coalgebra can be embedded in a symmetric coalgebra. A dual version of Brauer's equivalence theorem is presented, allowing a characterization of symmetric coalgebras by comparing certain func...

Here we initiate an investigation of the equational classes of m– symmetric algebras endowed with two tense operators. These varieties is a generalization of tense algebras. Our main interest is the duality theory for these classes of algebras. In order to do this, we require Urquart’s duality for Ockham algebras and Goldblatt’s duality for bounded distributive lattice with operations. The dual...

Abstract We show that intuitionistic logic is deductively equivalent to Connexive Heyting Logic ( $$\textrm{CHL}$$ CHL ), hereby introduced as an example of a strongly connexive with intuitive semantics. use the reverse algebraisation paradigm: presented assertional point regular variety (whose structur...

The variety \(\mathbb{DHMSH}\) of dually hemimorphic semi-Heyting algebras was introduced in 2011 by the second author as an expansion a dual hemimorphism. In this paper, we focus on from logical point view. paper presents extensive investigation logic corresponding to and its axiomatic extensions, along with equally universal algebraic study their semantics. Firstly, present Hilbert-style axio...

We begin by defining tensor products of vector spaces over a field and then we investigate some basic properties of these tensors, in particular the existence of bases and duality. After this, we investigate special kinds of tensors, namely, symmetric tensors and skew-symmetric tensors. Tensor products of modules over a commutative ring with identity will be discussed very briefly. They show up...

Extending early work, we formulate the large N matrix mechanics of general bosonic, fermionic and supersymmetric matrix models, including Matrix theory: The Hamiltonian framework of large N matrix mechanics provides a natural setting in which to study the algebras of the large N limit, including (reduced) Lie algebras, (reduced) super-symmetry algebras and free algebras. We find in particular a...

Any finite distributive lattice has a unique Heyting structure. Every finite Heyting semilattice has, of course, a unique lattice structure and it is necessarily distributive. ∗ This ms was born in 2002. The first appendix was added in 2005, the first footnote in 2013, the subscorings in 2015 and the addendum in 2017. 1 [ ] See 2nd appendix for subscorings. First x and y meet x↔ y in the same w...

Connections between annihilators and ideals in Frobenius and symmetric algebras are used to provide a new proof of a result of Nakayama on quotient algebras, and an application is given to central symmetric algebras. 2010 Mathematics subject classification: primary 16D99; secondary 15A63.

Abstract In Hyland et al. (1980), Hyland, Johnstone and Pitts introduced the notion of tripos for purpose organizing construction realizability toposes in a way that generalizes localic from complete Heyting algebras. (2002), one finds generalization this eliminating an unnecessary assumption (1980). The aim paper is to characterize triposes over base topos ${\cal S}$ terms so-called constant o...