Indecomposable baric algebras

Costa, Rogério A.; Guzzo, Henrique

doi:10.1016/0024-3795(93)90434-p

Cited by 27 publications

(25 citation statements)

References 15 publications

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“…In this work we define a new way to construct a baric algebra starting from two given baric algebras. Our construction, although similar, is different than that in [1]. In particular, while the construction in [1] always gives rise to decomposable baric algebras, we will show that in the commutative unital case our construction preserves indecomposability.…”

Section: Introductionmentioning

confidence: 76%

“…In [1] the notion of decomposable baric algebra was introduced. Namely, a baric algebra (A, ω) with an idempotent of weight 1 is decomposable if there are non-trivial ideals N 1 and N 2 of A, both contained in Ker ω and such that…”

Section: èöóôó× ø óò 51º Let I a I Be An Ideal Then I Is An Ideal Ofmentioning

confidence: 99%

“…In [1] the notion of decomposable baric algebras was introduced. 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.…”

Section: Introductionmentioning

confidence: 99%

“…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%

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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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Section: Introductionmentioning

confidence: 76%

Section: èöóôó× ø óò 51º Let I a I Be An Ideal Then I Is An Ideal Ofmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Tying up baric algebras

Oller-Marcén

2012

Mathematica Slovaca

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“…A random sampling of current references might include Wörz-Busekros [37]; Walcher [33]; Guzzo [18], [19]; Costa and Guzzo [7], [8]; Hentzel, Peresi, and Holgate [21]; Peresi [31]; Cortés [6]; Martinez [28]; Burgueño, Neuberg, and Suazo [5]; González and Martinez [16]; and González, Martinez, and Vicente [17]. This list is by no means complete, but it does provide a starting point for some of the current work being done in the field.…”

Section: Resultsmentioning

confidence: 99%

Algebraic structure of genetic inheritance

Reed

1997

Bull. Amer. Math. Soc.

113

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Abstract. In this paper we will explore the nonassociative algebraic structure that naturally occurs as genetic information gets passed down through the generations. While modern understanding of genetic inheritance initiated with the theories of Charles Darwin, it was the Augustinian monk Gregor Mendel who began to uncover the mathematical nature of the subject. In fact, the symbolism Mendel used to describe his first results (e.g., see his 1866 paper Experiments in Plant-Hybridization [30]) is quite algebraically suggestive. Seventy four years later, I.M.H. Etherington introduced the formal language of abstract algebra to the study of genetics in his series of seminal papers [9], [10], [11]. In this paper we will discuss the concepts of genetics that suggest the underlying algebraic structure of inheritance, and we will give a brief overview of the algebras which arise in genetics and some of their basic properties and relationships. With the popularity of biologically motivated mathematics continuing to rise, we offer this survey article as another example of the breadth of mathematics that has biological significance. The most comprehensive reference for the mathematical research done in this area (through 1980) is .

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The bar-radical of baric algebras

Guzzo

1996

Arch. Math

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Indecomposable baric algebras

Cited by 27 publications

References 15 publications

Tying up baric algebras

Tying up baric algebras

Algebraic structure of genetic inheritance

The bar-radical of baric algebras

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