Connections Techniques in Graded Morita Rings Theory

Abstract

We introduce connections in the restricted support of the grading techniques in the context of graded Morita rings $\mathfrak{R}$ in order to begin the study of its structure. As a consequence, we show that if the initial couple of bimodules have their 0-homogeneous components tight and the initial pairings are onto, then $\mathfrak{R}$ decomposes as the direct sum of (graded) ideals

$$\displaystyle{\mathfrak{R} =\bigoplus \limits _{i\in I}\mathfrak{R}_{i},}$$

where any $\mathfrak{R}_{i}$ is a graded Morita ring. Furthermore, $\mathfrak{R}_{i}\mathfrak{R}_{j} = 0$ whence i ≠ j.