Each row of MΓ is in the space V⊕V⊕⋯⊕V (where there are n1 copies of V) and so, for example, rankMΓ⩽n1dimV. Suppose that E is an n1×n1 invertible matrix, and let 1 be the n2×n2 identity matrix. Then, rankM(E⊗1)=rankM and rank[M(E⊗1)]Γ=rankMΓ(E...
V. Grishin and V. V.\nShchigolev, respectively. For example, we prove that a unital algebra\n$F^{(n)}_2$ $(n\\geqslant 4)$ over a field $K$ of characteristic $p\\geqslant n$\npossesses a finite strictly descending "composition" series of T-ideals\n$T^{(3)}=T_1\\supset ...
If A is an elliptic curve defined over R, let A(R)0 denote the connected compo- nent of the identity in A(R). Lemma 5. Suppose A is an elliptic curve over R, P1, . . . , Pr ∈ A(R)0 are Z- linearly independent in A(R)/A(R)tors, and U is an open subset of A(R...