A classical result of Noncommutative Algebra due to I. Niven, N. Jacobson and R. Baer asserts that an associative noncommutative division ring D has finite dimension over its center R and is algebraically closed (that is, every nonconstant polynomial in one indeterminate with left, or right, coefficients in D has a root in D) if and only if R is a real closed field and D is isomorphic to the ri...

we show that every semi-artinian module which is contained in a direct sum of finitely presented modules in $si[m]$, is weakly co-semisimple if and only if it is regular in $si[m]$. as a consequence, we observe that every semi-artinian ring is regular in the sense of von neumann if and only if its simple modules are $fp$-injective.

Abstract. In this paper, we summarize the work published in [1, 2, 3]. Based on a simple stochastic model, a general framework for modelling diffuse interface flows is derived. This allows to both define a continuous Baer and Nunziato type model depending only on one free parameter, and to derive a numerical scheme, which is actually a discontinuous Galerkin extension of [4]. The numerical sche...

we show  that a projective maximal submodule of afinitely generated, regular, extending module is a directsummand. hence, every finitely generated, regular, extendingmodule with projective maximal submodules is semisimple. as aconsequence, we observe that every regular, hereditary, extendingmodule is semisimple. this generalizes and simplifies a result of  dung and   smith. as another consequen...