Explicit Super-Linear Algebra over K[θ1, θ2]: A General Berezinian Correction Formula and Multiplicativity Theorem for Arbitrary Block Size

We study super-matrices $M_{m|n}(R)$ over the rank-two exterior algebra $R=K[θ_1,θ_2]/(θ_1^2,θ_2^2,θ_1θ_2+θ_2θ_1)$, the smallest supercommutative ring on which the Berezinian's odd-by-odd correction term $BD^{-1}C$ need not vanish. We recall that the supertrace satisfies graded cyclicity, $\mathrm{s