| Popis: |
Let K be a field (finite or infinite) of char ( K ) ≠ 2 and let U T 2 ( K ) be the 2 × 2 upper triangular matrix algebra over K. If ⋅ is the usual product on U T 2 ( K ) then with the new product a ∘ b = ( 1 / 2 ) ( a ⋅ b + b ⋅ a ) we have that U T 2 ( K ) is a Jordan algebra, denoted by U J 2 = U J 2 ( K ) . In this paper, we describe the set I of all polynomial identities of U J 2 and a linear basis for the corresponding relatively free algebra. Moreover, if K is infinite we prove that I has the Specht property. In other words I, and every T-ideal containing I, is finitely generated as a T-ideal. |
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