On $\mathcal{T}$-$\delta$-noncosingular modules

In this paper, we introduce and study the notion of $\mathcal{T}$-$\delta$-noncosingular modules. The aim of this paper is to present some applications. Let $R$ be a commutative ring. If $R_{R}$ is $\mathcal{T}$-$\delta$-noncosingular, we show right $R_{R}$ is nonsingular. Also we prove that any singular regular module is an $\mathcal{T}$-$\delta$-noncosingular module.