Irresolute \(\beta\)-topological Algebra

In this paper, we introduce a generalization of topological \(R\)-module using \(\beta\)-open sets called irresolute \(\beta\)-topological algebra (group, ring, and module). We show that the center of an irresolute \(\beta\)-hausdorff ring is \(\beta\)-closed and if \(N\) is \(Q\)-submodule of an irresolute \(\beta\)-topological \(R\)-module \(M\), then \(\beta Cl(N)_M\) is also \(\beta Cl(Q)_R\)-submodule where \(Q,N\) are subsets of \(R,M\) respectively. Several other properties of them are investigated.