Georgian Mathematical Journal ( IF 0.500 ) Pub Date : 2020-07-16 , DOI: 10.1515/gmj-2020-2068
Antonio J. Calderón Martín

Let $(ℌ,μ,α)$ be a regular Hom-algebra of arbitrary dimension and over an arbitrary base field $𝔽$. A basis $ℬ={ei}i∈I$ of $ℌ$ is called multiplicative if for any $i,j∈I$, we have that $μ⁢(ei,ej)∈𝔽⁢ek$ and $α⁢(ei)∈𝔽⁢ep$ for some $k,p∈I$. We show that if $ℌ$ admits a multiplicative basis, then it decomposes as the direct sum $ℌ=⊕rℑr$ of well-described ideals admitting each one a multiplicative basis. Also, the minimality of $ℌ$ is characterized in terms of the multiplicative basis and it is shown that, in case $ℬ$, in addition, it is a basis of division, then the above direct sum is composed by means of the family of its minimal ideals, each one admitting a multiplicative basis of division.

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