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Let $\mathbb{A}_n^m$ be an arbitrary $n$-dimensional commutative associativealgebra over the field of complex numbers with $m$ idempotents. Let$e_1=1,e_2,\ldots,e_k$ with $2\leq k\leq 2n$ be elements of $\mathbb{A}_n^m$which are linearly independent over the field of real numbers. We considermonogenic (i.e. continuous and differentiable in the sense of Gateaux)functions of the variable $\sum_{j=1}^k x_j\,e_j$, where $x_1,x_2,\ldots,x_k$are real, and we prove curvilinear analogues of the Cauchy integral theorem,the Morera theorem and the Cauchy integral formula in $k$-dimensional ($2\leqk\leq 2n$) real subset of the algebra $\mathbb{A}_n^m$. The present article isgeneralized of the author's paper [1], where mentioned results are obtained for$k=3$.

Integral theorems for monogenic functions in commutative algebras