By Yurij A. Drozd, Vladimir V. Kirichenko (auth.)
This English variation has an extra bankruptcy "Elements of Homological Al gebra". Homological tools seem to be powerful in lots of difficulties within the conception of algebras; we are hoping their inclusion makes this ebook extra whole and self-contained as a textbook. we now have additionally taken this party to right a number of inaccuracies and error within the unique Russian variation. we must always prefer to convey our gratitude to V. Dlab who has not just metic ulously translated the textual content, yet has additionally contributed by means of writing an Appendix dedicated to a brand new very important category of algebras, viz. quasi-hereditary algebras. eventually, we're indebted to the publishers, Springer-Verlag, for allowing this booklet to arrive this kind of extensive viewers on this planet of mathematical group. Kiev, February 1993 Yu.A. Drozd V.V. Kirichenko Preface the speculation of finite dimensional algebras is among the oldest branches of contemporary algebra. Its beginning is associated with the paintings of Hamilton who chanced on the well-known algebra of quaternions, and Cayley who constructed matrix concept. Later finite dimensional algebras have been studied via a lot of mathematicians together with B. Peirce, C.S. Peirce, Clifford, ·Weierstrass, Dedekind, Jordan and Frobenius. on the finish of the final century T. Molien and E. Cartan defined the semisimple algebras over the advanced and actual fields and paved the 1st steps in the direction of the examine of non-semi uncomplicated algebras.