Some New Characteristics of Topological Ring-Groupoids - Majeed, Taghreed Hur (Iraqi Journal of Science, 2026)
The main goal of this work is to study some new characteristics of groupoids ring of algebraic topology, and we started with algebraic cases and simple topology, but it is vital as information background for comparing what we found as a result and if we focused in our study on the topological projective ring groupoid and topological projective cover. Taylor Robert, who talked about groupoid and topological groupoids was the start of the topological group groupoid and topological groupoid rings. The relationship between topological projective groupoid ring and topological group groupoid was developed. We used the definitions, previous relationships topological projective groupoids ring, topological group groupoid, projective cover and topological projective ring harmonious with our work. Many results regarding the topological projective cover for the topological projective groupoids ring and the partial topological projective groupoid ring and topological ring quotient groupoid are obtained. We applied some structures to clarify the relationships between those different spaces. Lastly, we studied the direction summation of equations that forms the topological projective cover of topological projective groupoid rings is the orderly highlighted guidelines such that we proved the final number of the direct sum for the topological groupoid covers ring is the cover of topological groupoid ring.