Gladys Chalom - Academia.edu (original) (raw)

Papers by Gladys Chalom

We dedicate this work to the memory of Sheila Brenner. Abstract: The purpose of this work is to s... more We dedicate this work to the memory of Sheila Brenner. Abstract: The purpose of this work is to show that if Λ a strongly simply connected semi-regular iterated tubular algebra and M is an indecomposable Λ-module then Λ[M] is tame if and only if qΛ[M] is weakly non negative. Key Words: representation type e quadratic forms.

We consider binary abelian codes of length p n q m where p and q are prime rational integers unde... more We consider binary abelian codes of length p n q m where p and q are prime rational integers under some restrictive hypotheses. In this case, we determine the idempotents generating minimal codes and either the respective weights or bounds of these weights. We give examples showing that these bounds are attained in some cases. Index Terms-group algebra, code weight, primitive idempotent, minimal abelian codes.

Revista De La Union Matematica Argentina, 2007

We will introduce very briefly the homogenization process in the commutative case, just to explai... more We will introduce very briefly the homogenization process in the commutative case, just to explain the main motivation of our work. In the commutative context, the Buchberger Algorithm give us a very direct strategy for computing Grobner Basis for a given ideal I ∈ k[x1, x2, . . . , xn]: we consider a finite set {f1, f2, ...fk} of generators of I, compute the S polynomials, for any pair i,j, reduce them, and if the remainder is non zero, add this remainder to the list of the given polynomials, to make all the S polynomials reduce to zero. Although this process always finish, in the commutative case, it can be very inefficient and time consuming, by instance getting S polynomials of much higher degree that the ones we begin with. It is easy to see ( see [1]) that if we begin with a set of homogeneos polynomials this problem does not occur and the S polynomials we obtain are again homogeneous. So, lets define this process for Λ = k[x1, x2, . . . , xn]: Let f ∈ Λ and w a new variable. ...

ArXiv, 2012

We consider binary abelian codes of length pmqnp^m q^npmqn, where ppp and qqq are prime rational intege... more We consider binary abelian codes of length pmqnp^m q^npmqn, where ppp and qqq are prime rational integers under some restrictive hypotheses. In this case, we determine the idempotents generating minimal codes and either the respective weights or bounds of these weights. We give examples showing that these bounds are attained in some cases.

We consider binary abelian codes of lengthpq where p and q are prime rational integers under some... more We consider binary abelian codes of lengthpq where p and q are prime rational integers under some restrictive hypotheses. In this case, we determine the idempotents gene rating minimal codes and either the respective weights or bounds of these weights. We give examples showing that these bounds ar e attained in some cases.

São Paulo Journal of Mathematical Sciences

São Paulo Journal of Mathematical Sciences, 2016

We consider binary abelian codes of length pmqnp^m q^npmqn, where ppp and qqq are prime rational intege... more We consider binary abelian codes of length pmqnp^m q^npmqn, where ppp and qqq are prime rational integers under some restrictive hypotheses. In this case, we determine the idempotents generating minimal codes and either the respective weights or bounds of these weights. We give examples showing that these bounds are attained in some cases.

Lecture Notes in Pure and Applied Mathematics, 2006

Irreducible morphisms in subcategories Gladys Chalom and Hector Merklen Instituto de Matematica e... more Irreducible morphisms in subcategories Gladys Chalom and Hector Merklen Instituto de Matematica e Estatıstica, Universidade de Sao Paulo, Caixa Postal 66281, Sao ... of all Λ− modules; –mod− Λ is the category of all finitely generated Λ− modules; –a Krull-Schmidt category A ...

Boletim da Sociedade Paranaense de Matemática, 2009

The purpose of this work is to show that if Λ a strongly simply connected semi-regular iterated t... more The purpose of this work is to show that if Λ a strongly simply connected semi-regular iterated tubular algebra and M is an indecomposable Λmodule then Λ[M ] is tame if and only if q Λ[M ] is weakly non negative.

Communications in Algebra, 2000

We define essential idempotents in group algebras and use them to prove that every mininmal abeli... more We define essential idempotents in group algebras and use them to prove that every mininmal abelian
non-cyclic code is a repetition code. Also we use them to prove that every minimal abelian code is
equivalent to a minimal cyclic code of the same length. Finally, we show that a binary cyclic code is
simplex if and only if is of length of the form n=2k−1n = 2^k-1n=2k−1 and is generated by an essential idempotent.

We dedicate this work to the memory of Sheila Brenner. Abstract: The purpose of this work is to s... more We dedicate this work to the memory of Sheila Brenner. Abstract: The purpose of this work is to show that if Λ a strongly simply connected semi-regular iterated tubular algebra and M is an indecomposable Λ-module then Λ[M] is tame if and only if qΛ[M] is weakly non negative. Key Words: representation type e quadratic forms.

We consider binary abelian codes of length p n q m where p and q are prime rational integers unde... more We consider binary abelian codes of length p n q m where p and q are prime rational integers under some restrictive hypotheses. In this case, we determine the idempotents generating minimal codes and either the respective weights or bounds of these weights. We give examples showing that these bounds are attained in some cases. Index Terms-group algebra, code weight, primitive idempotent, minimal abelian codes.

Revista De La Union Matematica Argentina, 2007

We will introduce very briefly the homogenization process in the commutative case, just to explai... more We will introduce very briefly the homogenization process in the commutative case, just to explain the main motivation of our work. In the commutative context, the Buchberger Algorithm give us a very direct strategy for computing Grobner Basis for a given ideal I ∈ k[x1, x2, . . . , xn]: we consider a finite set {f1, f2, ...fk} of generators of I, compute the S polynomials, for any pair i,j, reduce them, and if the remainder is non zero, add this remainder to the list of the given polynomials, to make all the S polynomials reduce to zero. Although this process always finish, in the commutative case, it can be very inefficient and time consuming, by instance getting S polynomials of much higher degree that the ones we begin with. It is easy to see ( see [1]) that if we begin with a set of homogeneos polynomials this problem does not occur and the S polynomials we obtain are again homogeneous. So, lets define this process for Λ = k[x1, x2, . . . , xn]: Let f ∈ Λ and w a new variable. ...

ArXiv, 2012

We consider binary abelian codes of length pmqnp^m q^npmqn, where ppp and qqq are prime rational intege... more We consider binary abelian codes of length pmqnp^m q^npmqn, where ppp and qqq are prime rational integers under some restrictive hypotheses. In this case, we determine the idempotents generating minimal codes and either the respective weights or bounds of these weights. We give examples showing that these bounds are attained in some cases.

We consider binary abelian codes of lengthpq where p and q are prime rational integers under some... more We consider binary abelian codes of lengthpq where p and q are prime rational integers under some restrictive hypotheses. In this case, we determine the idempotents gene rating minimal codes and either the respective weights or bounds of these weights. We give examples showing that these bounds ar e attained in some cases.

São Paulo Journal of Mathematical Sciences

São Paulo Journal of Mathematical Sciences, 2016

We consider binary abelian codes of length pmqnp^m q^npmqn, where ppp and qqq are prime rational intege... more We consider binary abelian codes of length pmqnp^m q^npmqn, where ppp and qqq are prime rational integers under some restrictive hypotheses. In this case, we determine the idempotents generating minimal codes and either the respective weights or bounds of these weights. We give examples showing that these bounds are attained in some cases.

Lecture Notes in Pure and Applied Mathematics, 2006

Irreducible morphisms in subcategories Gladys Chalom and Hector Merklen Instituto de Matematica e... more Irreducible morphisms in subcategories Gladys Chalom and Hector Merklen Instituto de Matematica e Estatıstica, Universidade de Sao Paulo, Caixa Postal 66281, Sao ... of all Λ− modules; –mod− Λ is the category of all finitely generated Λ− modules; –a Krull-Schmidt category A ...

Boletim da Sociedade Paranaense de Matemática, 2009

The purpose of this work is to show that if Λ a strongly simply connected semi-regular iterated t... more The purpose of this work is to show that if Λ a strongly simply connected semi-regular iterated tubular algebra and M is an indecomposable Λmodule then Λ[M ] is tame if and only if q Λ[M ] is weakly non negative.

Communications in Algebra, 2000

We define essential idempotents in group algebras and use them to prove that every mininmal abeli... more We define essential idempotents in group algebras and use them to prove that every mininmal abelian
non-cyclic code is a repetition code. Also we use them to prove that every minimal abelian code is
equivalent to a minimal cyclic code of the same length. Finally, we show that a binary cyclic code is
simplex if and only if is of length of the form n=2k−1n = 2^k-1n=2k−1 and is generated by an essential idempotent.