Abstract:We build up a multiplicative basis for a locally adequate concordant semigroup algebra by constructing Rukolaȋne idempotents. This allows us to decompose the locally adequate concordant semigroup algebra into a direct product of primitive abundant 0-J -simple semigroup algebras. We also deduce a direct sum decomposition of this semigroup algebra in terms of the R -classes of the semigroup obtained from the above multiplicative basis. Finally, for some special cases, we provide a description of the projective indecomposable modules and determine the representation type.
This paper is devoted to the global well-posedness of a threedimensional Stokes-Magneto equations with fractional magnetic diffusion. It is proved that the equations admit a unique global-in-time strong solution for arbitrary initial data when the fractional index α ≥ 3 2 . This result might have a potential application in the theory of magnetic relaxtion.
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