EUDML

A class ℱ of universal algebras is called a formation if the following conditions are satisfied: 1) Any homomorphic image of A ∈ ℱ is in ℱ; 2) If α₁, α₂ are congruences on A and $A / α_{i} \in ℱ$ , i = 1,2, then A/(α₁∩α₂) ∈ ℱ. We prove that any formation generated by a simple algebra with permutable congruences is minimal, and hence any formation containing a simple algebra, with permutable congruences, contains a minimum subformation. This result gives a partial answer to an open problem of Shemetkov and Skiba...

The structure of left C-rpp semigroups.

K.P. Shum; G. Yuqi; Z. Pinyu — 1995

Semigroup forum

Vague ideals of implication groupoids

Ravi Kumar Bandaru; K.P. Shum — 2013

Discussiones Mathematicae - General Algebra and Applications

We introduce the concept of vague ideals in a distributive implication groupoid and investigate their properties. The vague ideals of a distributive implication groupoid are also characterized.

Congruences and Boolean filters of quasi-modular p-algebras

Abd El-Mohsen Badawy; K.P. Shum — 2014

Discussiones Mathematicae - General Algebra and Applications

The concept of Boolean filters in p-algebras is introduced. Some properties of Boolean filters are studied. It is proved that the class of all Boolean filters BF(L) of a quasi-modular p-algebra L is a bounded distributive lattice. The Glivenko congruence Φ on a p-algebra L is defined by (x,y) ∈ Φ iff x** = y**. Boolean filters [Fₐ), a ∈ B(L) , generated by the Glivenko congruence classes Fₐ (where Fₐ is the congruence class [a]Φ) are described in a quasi-modular p-algebra L. We observe that the...

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On p.p.-rings which are reduced.

Reduced p.p.-rings without identity.

Retract extensions of ordered sets.

On matrix rings over unit-regular rings.

Lattices of order ideals on ordered semigroups.

Homomorphisms of implicative semigroups.

Hereditary torsion classes of S-systems.

Prime radical theorem on ordered semigroups.

Minimal formations of universal algebras

The structure of left C-rpp semigroups.

Vague ideals of implication groupoids

Congruences and Boolean filters of quasi-modular p-algebras