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