Geodesic
On representation of $k$-valued logic functions by a~sum of products of subfunctions
Diskretnaya Matematika, Tome 19 (2007) no. 2, pp. 94-100.

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The set of variables of a $k$-valued logic function $f(x_1,\dots,x_n)$ is partitioned into $t$ parts, $t>1$, and a polynomial representation of the function $f$ is considered where the terms are products of all possible subfunctions corresponding to the partitioning. We analyse conditions under which an arbitrary function admits a representation in such a polynomial form. 
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V. I. Panteleev; N. A. Peryazev. On representation of $k$-valued logic functions by a~sum of products of subfunctions. Diskretnaya Matematika, Tome 19 (2007) no. 2, pp. 94-100. http://geodesic.mathdoc.fr/item/DM_2007_19_2_a10/

[1] Zhegalkin I. I., “Arifmetizatsiya simvolicheskoi logiki”, Matem. sb., 36 (1929), 205–338 | Zbl

[2] Vinokurov S. F., Peryazev N. A., “Razlozhenie bulevykh funktsii v summu proizvedenii sobstvennykh podfunktsii”, Diskretnaya matematika, 5:3 (1993), 102–104 | MR | Zbl

[3] Skornyakov L. A., Dedekindovy struktury s dopolneniyami i regulyarnye koltsa, Fizmatgiz, Moskva, 1961

[4] Goodearl K. R., Von Neumann regular rings, Pitman, London, 1979 | MR | Zbl

[5] Vinokurov S. F., Panteleev V. I., “Polinomialnoe predstavlenie bulevykh funktsii s ispolzovaniem tolko ostatochnykh funktsii”, Trudy XII Baikalskoi mezhdunarodnoi konf., t. 5, Irkutsk, 2001, 27–31