Not every equational class of infinitary algebras contains a simple algebra

Infinitary Initial Algebra Specifications for Stream Algebras

Coinductive Foundations of Infinitary Rewriting and Infinitary Equational Logic

We present a coinductive framework for defining and reasoning about the infinitary analogues of equational logic and term rewriting in a uniform way. We define ∞ =, the infinitary extension of a given equational theory =R, and →∞, the standard notion of infinitary rewriting associated to a reduction relation →R, as follows: ∞ = := νR. (=R ∪ R) → := μR. νS. (→R ∪ R) ; S Here μ and ν are the leas...

A Bound for the Nilpotency Class of a Lie Algebra

In the present paper, we prove that if L is a nilpotent Lie algebra whose proper subalge- bras are all nilpotent of class at most n, then the class of L is at most bnd=(d 1)c, where b c denotes the integral part and d is the minimal number of generators of L.

A new branch of the logical algebra: UP-algebras

In this paper, we introduce a new algebraic structure, called a UP-algebra (UP means the University of Phayao) and a concept of UP-ideals, UP-subalgebras, congruences and UP-homomorphisms in UP-algebras, and investigated some related properties of them. We also describe connections between UP-ideals, UP-subalgebras, congruences and UP-homomorphisms, and show that the notion of UP-algebras is a ...

Equational Logic and Equational Theories of Algebras