Computation of generalized inverses of tensors via <i>t</i> ?product

Generalized inverses of tensors play increasingly important roles in computational mathematics and numerical analysis. It is appropriate to develop the theory generalized within algebraic structure a ring. In this paper, we study different over commutative ring noncommutative Several examples are provided support theoretical results. We also propose algorithms for computing inner inverses, Moore–Penrose inverse, weighted inverse The prowess some results demonstrated by applying these ideas solve an image deblurring problem.