Finite basis problem for identities with involution

2014/10/08 by Irina Sviridova, Sviridova, Irina
Computer Science · Mathematics · #16R50 #16W10 #16W20 #16W50 #16W55 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Matrix Theory and Algorithms #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1410.2233

openalex publication_date 2014/10/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider associative algebras with involution over a field of characteristic zero. We proved that any algebra with involution satisfies the same identities with involution as the Grassmann envelope of some finite dimensional Z₄-graded algebra with graded involution. As a consequence we obtain the positive solution of the Specht problem for identities with involution: any associative algebra with involution over a field of characteristic zero has a finite basis of identities with involution. These results are analogs of theorems of A.R.Kemer for ordinary identities.

Citations

• Representability and Specht problem for G-graded algebras

Related

• Finitely generated algebras with involution and their identities
• Identities of finitely generated graded algebras with involution
• \ℤ₂-graded identities of the Grassmann algebra over a\n finite field
• One proof of the original Kemer's theorems (concerning the text of C. Procesi "What happened to PI-theory", arxiv.org/abs/1403.5673)
• ℤ₂-graded identities of the Grassmann algebra over a finite field (update version)