Wedderburn–Malcev decomposition of one-sided ideals of finite dimensional algebras

ABSTRACT

Let A be a finite dimensional associative algebra over a perfect field and let R be the radical of A. We show that for every one-sided ideal I of A there exists a semisimple subalgebra S of A such that $I=I_S\oplus I_R$ where I_S = I∩S and I_R = I∩R.

KEYWORDS:

• Finite dimensional algebra
• one-sided ideals
• Wedderburn–Malcev decomposition

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 16P10
• 16D20
• 16D25

Acknowledgments

Supported by University of Leicester. Supported by the Higher Committee for Educational Development in Iraq (HCED Iraq).