Characterizing primes in some noncommutative rings

For a ring R with identity 1, a preprime is a nonempty subset T of R which is closed under the two binary operations, addition and multiplication, of R and with -10 T. A prime of R is a preprime of R which is maximal with respect to set inclusion.A field K is locally finite if every member of K is a member of some finite subfield of K.For a finite dimensional vector space V over K let © = Hom^ (V, V) denote the full ring of linear transformations of V over K. Let W and L be subspaces of V with WaLaV aud W Φ L. Let T(L,W) = {ae@>la Lc:W}.Then T(L 9 W) is a preprime of ©.Let = {T(L, W)IW, L are subspaces of V, WaL,W Ψ L]We will show that the primes of (S are exactly those preprimes T(L, W)e^~ with dim* L = 1 4-dim* W.