  The Dimensional Regularization of Bollini and Giambiags (Phys. Lett. {\bf B
40}, 566 (1972), Il Nuovo Cim. {\bf B 12}, 20 (1972). Phys. Rev. {\bf D 53},
5761 (1996)) can not be defined for all Schwartz Tempered Distributions
Explicitly Lorentz Invariant (STDELI) ${\cal S}^{'}_L$. In this paper we
overcome here such limitation and show that it can be generalized to all
aforementioned STDELI and obtain a product in a ring with zero divisors.
  For this purpose, we resort to a formula obtained in [Int. J. of Theor. Phys.
{\bf 43}, 1019 (2004)] and demonstrate the existence of the convolution (in
Minkowskian space) of such distributions. This is done by following a procedure
similar to that used so as to define a general convolution between the
Ultradistributions of J. Sebastiao e Silva [Math. Ann. {\bf 136}, 38 (1958)],
also known as Ultrahyperfunctions, obtained by Bollini et al. [Int. J. of
Theor. Phys. {\bf 38}, 2315 (1999), {\bf 43}, 1019 (2004), {\bf 43}, 59
(2004),{\bf 46}, 3030 (2007)]. Using the Inverse Fourier Transform we get the
ring with zero divisors ${\cal S}^{'}_{LA}$, defined as ${\cal
S}^{'}_{LA}={\cal F}^{-1}\{{\cal S}^{'}_L\}$, where ${\cal F}^{-1}$ denotes the
Inverse Fourier Transform. In this manner we effect a dimensional
regularization in momentum space (the ring ${\cal S}^{'}_{L}$) via convolution,
and a product of distributions in the corresponding configuration space (the
ring ${\cal S}^{'}_{LA})$. This generalizes the results obtained by Bollini and
Giambiagi for Euclidean space in [Phys. Rev. {\bf D 53}, 5761 (1996)].
  We provide several examples of the application of our new results in Quantum
Field Theory. In particular, the convolution of $n$ massless Feynman
propagators and the convolution of n massless Wheeler propagators in
Minkowskian space.
