Indecomposable baric algebras. II

“…a 1 ) = ϕ(a 1 , 0) and ϕ 2 (a 2 ) = ϕ(0, a 2 ). It is easy to check that both ϕ i are K-homomorphisms and ϕ(a 1 , a 2 a 2 )(b 1 , b 2 ) and thus, by the preceding considerations:…”

Section: Uniqueness Of the Weight Homomorphismmentioning

confidence: 86%

“…In the same paper it was also presented a way to construct decomposable baric algebras starting from two baric algebras with an idempotent of weight one. Furthermore in [1] and in [2] the author analized the indecomposability of some well-known examples of algebras arising in genetics. In this work we define a new way to construct a baric algebra starting from two given baric algebras.…”

Section: Introductionmentioning

confidence: 99%

Tying up baric algebras

Oller-Marcén

2012

Mathematica Slovaca

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ABSTRACT. Given two baric algebras (A 1 , ω 1 ) and (A 2 , ω 2 ) we describe a way to define a new baric algebra structure over the vector space A 1 ⊕ A 2 , which we shall denote (A 1 A 2 , ω 1 ω 2 ). We present some easy properties of this construction and we show that in the commutative and unital case it preserves indecomposability. Algebras of the form A 1 A 2 in the associative, coutabledimensional, zero-characteristic case are classified.

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“…Therefore by [13], ( A/I,ω) is a Bernstein-Jordan algebra. By [7], rad(A/I) = bar( A/I) 2 = bar( A)/I 2 = 0.…”

Section: Where a I ∈ (Bar( A)) K−2 And B I ∈ Bar( A)mentioning

confidence: 99%

“…Clearly x [n+2] = (ω(x)) 2 n x [n+1] , for all x ∈ C. Then by [1] and [2], B ∨ C is a n th -order Bernstein algebra, where B is the Example 4.2.…”

Section: Proposition 45 Let ( a ω) Be A Jordan And N Th -Order Bermentioning

confidence: 99%