12 citations · 21 across the 6 of their papers we have counts for
8 papers
Left reductive regular semigroups
P. A. Azeef Muhammed, Gracinda M. S. Gomes
In this paper we develop an ideal structure theory for the class of left reductive regular semigroups and apply it to several subclasses of popular interest. In these classes we ob…
Cross-connections in Clifford semigroups
P. A. Azeef Muhammed, C. S. Preenu
An inverse Clifford semigroup (often referred to as just a Clifford semigroup) is a semilattice of groups. It is an inverse semigroup and in fact, one of the earliest studied class…
The mathematical work of K.S.S. Nambooripad
John Meakin, P. A. Azeef Muhammed, A. R. Rajan
We provide an overview of the mathematical work of K.S.S. Nambooripad, with a focus on his contributions to the theory of regular semigroups. In particular, we outline Nambooripad'…
Cross-connection structure of locally inverse semigroups
P. A. Azeef Muhammed, M. V. Volkov, K. Auinger
Locally inverse semigroups are regular semigroups whose idempotents form pseudo-semilattices. We characterise the categories that correspond to locally inverse semigroups in the re…
A Tale of Two Categories: Inductive groupoids and Cross-connections
P. A. Azeef Muhammed, Mikhail V. Volkov
A groupoid is a small category in which all morphisms are isomorphisms. An inductive groupoid is a specialised groupoid whose object set is a regular biordered set and the morphism…
Cross-connection structure of concordant semigroups
P. A. Azeef Muhammed, P. G. Romeo, K. S. S. Nambooripad
Cross-connection theory provides the construction of a semigroup from its ideal structure using small categories. A concordant semigroup is an idempotent-connected abundant semigro…
Inductive groupoids and cross-connections of regular semigroups
P. A. Azeef Muhammed, M. V. Volkov
There are two major structure theorems for an arbitrary regular semigroup using categories, both due to Nambooripad. The first construction using inductive groupoids departs from t…
Cross-connections and variants of the full transformation semigroup
P. A. Azeef Muhammed
Cross-connection theory propounded by K. S. S. Nambooripad describes the ideal structure of a regular semigroup using the categories of principal left (right) ideals. A variant $\m…