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Regular Hom-algebras admitting a multiplicative basis
Georgian Mathematical Journal ( IF 0.500 ) Pub Date : 2020-07-16 , DOI: 10.1515/gmj-2020-2068
Antonio J. Calderón Martín

Let (,μ,α) be a regular Hom-algebra of arbitrary dimension and over an arbitrary base field 𝔽. A basis ={ei}iI of is called multiplicative if for any i,jI, we have that μ(ei,ej)𝔽ek and α(ei)𝔽ep for some k,pI. We show that if admits a multiplicative basis, then it decomposes as the direct sum =rr of well-described ideals admitting each one a multiplicative basis. Also, the minimality of is characterized in terms of the multiplicative basis and it is shown that, in case , 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.
更新日期:2020-08-09

 

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