ON FREE IDEALS IN FREE ALGEBRAS OVER A COMMUTATIVE RING

Khurul Wardati, Indah Emilia Wijayanti, Sri Wahyuni

Abstract


Let A be a free R-algebra where R is a unital commutative ring. An ideal I in A is called a free ideal if it is a free R-submodule with the basis contained in the basis of A. The denition of free ideal and basic ideal in the free R-algebra are equivalent. The free ideal notion plays an important role in the proof of some special properties of a basic ideal that can characterize the free R-algebra. For example, a free R-algebra A is basically semisimple if and only if it is a direct sum of minimal basic ideals in A: In this work, we study the properties of basically semisimple free R-algebras.

DOI : http://dx.doi.org/10.22342/jims.21.1.170.59-69


Keywords


Free ideal, basic ideal, minimal basic ideal, basically semisimple algebra.

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References


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DOI: https://doi.org/10.22342/jims.21.1.170.59-69

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