P-algebras over multidimensional local fields

This article considers simple central algebras over multidimensional local algebras of exponent p, where p is the characteristic of the zero-dimensional residue field.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 175, pp. 121–127, 1989.In conclusion, the author would like to express his gratitude to Professor A. S. Merkur'ev for his attention and assistance.