19 papers
Ideal lattices of semigroup of doubly stochastic matrices
P G Romeo, Riya Jose
In this paper we illustrate the rule for finding number of idempotents in the doubly stochastic matrix and also locate the idempotents for the semigroups and . Fur…
Some ordered matrix semigroups
P. G. Romeo, Sathi P H
A semigroup together with compatible partial order is called an odered semigroup. In this paper we discuss the ordered matrix semigroups.
Ideal category of a Noetherian ring
P G Romeo, Minnumol P K
In this paper we describe the categories , [] whose objects are left [right] ideals of a Noetherian ring with unity and morphisms are appropriate $…
Normal categories of semigroup of order-preserving transformations on a finite chain
K K Sneha, P G Romeo
K. S. S. Nambooripad intoduced nornal categories to enable to describe the structure of regular semigroups fully. In this paper we describe the ideal categories of the regular semi…
On projective representations of Plesken Lie algebras
P G Romeo, Arjun S N
In this article we describe the projective representation of Plesken Lie algebras and equivalent central extensions of these algebras. Further it is also shown that there exists a…
Representation of Plesken Lie algebras
P. G. Romeo, S. N. Arjun
Cohen and Taylor introduced Plesken Lie algebras of finite groups and studied their structural properties. As a further step, we will introduce Plesken Lie algebra representations,…
Group lattices over division rings A tribute to the renowned Indian Mathematician K.S.S.Nambooripad
P. G. Romeo, Alanka Thomas
Group action on an algebraic structure gives a representation of the group by automorphisms on the structure. An action of a group on a lattice gives a group lattice. K.S.S. Namboo…
Chain Bundles and Category of Chains
P. G. Romeo, Riya Jose
In [7], we introduced the category of chain bundles with examples and established its significance. Here we shall describe certain categories which we call the category of chains i…
On category of Lie algebras
P G Romeo, Arjun S N
In this paper we describe the the category of Lie algebras of group algebras and the category of Plesken Lie algebras and explore the categorical relations between them. Further we…
Weakly Abundant Semigroups and variants
P G Romeo, Siji Michel
A weakly U abundant is a class of semigroups characterized using some generalized Green' relations. In this paper we discuss the variants of weakly U - abundant semigroups and it i…
On the embedding of Gamma-semigroup amalgam
Smisha M A, P G Romeo
Gamma-semigroup is introduced as a generalization of semigroups by M. K Sen and Saha. In this paper we describe amalgam of two Gamma-semigroups and discuss the embeddability of thi…
Generalized groups and module groupoids
P. G. Romeo, Sneha K K
In this paper we discuss generalized group, provides some interesting examples. Further we introduce a generalized module as a module like structure obtained from a generalized gro…
Biordered sets of lattices and homogeneous basis
P. G. Romeo, Akhila. R
In this paper we discuss the properties of the biordered set obtained from a complemented modular lattice and defines an operation using the sandwich elements of the biordered set.…
Graph inverse semigroups and their substructures
P G Romeo, Alanka Thomas
In this paper we discuss graph inverse semigroups which are constucted from a directed graphs and study several interesting properties of graph inverse semigroups such as the natur…
Category of chain bundles
P G Romeo, Riya Jose
For a category with subobjects and factorization, here we describe a new category which we call category of chain bundles and it is shown that this new category is also a category…
Local subsemigroups and variants of some class of semigroups
Siji Michael, P. G. Romeo
For an element a in a semigroup S the local subsemigroup of S with respect to a is the subsemigroup aSa of S and the variant of S with respect to a is a semigroup with underlying s…
Ideal categories of rings and ring of cones
Sreejamol P. R., P. G. Romeo
In this paper we describe the ideal category of a ring R as preadditive proper category. Further it is also shown that the cones in this category is a ring with appropriate additio…
Directed Graphs of Cayley Functions
Lejo J. Manavalan, P. G. Romeo
In this paper we describe a condition under which a given function that commute with an idempotent function on an infinite set is a Cayley function using its functional digraph.
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…