On Herstein's theorems relating modularity in A and A(+).

José A. Anquela

Extracta Mathematicae (1992)

  • Volume: 7, Issue: 1, page 5-8
  • ISSN: 0213-8743

Abstract

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In this paper we will examine the relationship between modularity in the lattices of subalgebras of A and A(+), for A an associative algebra over an algebraically closed field. To this aim we will construct an ideal which measures the modularity of an algebra (not necessarily associative) in paragraph 1, examine modular associative algebras in paragraph 2, and prove in paragraph 3 that the ideal constructed in paragraph 1 coincides for A and A(+). We will also examine some properties of the ideal mentioned in paragraph 1 when the algebras involved are Jordan.

How to cite

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Anquela, José A.. "On Herstein's theorems relating modularity in A and A(+).." Extracta Mathematicae 7.1 (1992): 5-8. <http://eudml.org/doc/39953>.

@article{Anquela1992,
abstract = {In this paper we will examine the relationship between modularity in the lattices of subalgebras of A and A(+), for A an associative algebra over an algebraically closed field. To this aim we will construct an ideal which measures the modularity of an algebra (not necessarily associative) in paragraph 1, examine modular associative algebras in paragraph 2, and prove in paragraph 3 that the ideal constructed in paragraph 1 coincides for A and A(+). We will also examine some properties of the ideal mentioned in paragraph 1 when the algebras involved are Jordan.},
author = {Anquela, José A.},
journal = {Extracta Mathematicae},
keywords = {Algebras de Jordan; Estructuras modulares; Retículos; Anillos no conmutativos; Jordan algebra; special Jordan algebra; lattice of subalgebras; modular lattice; radical ideal},
language = {eng},
number = {1},
pages = {5-8},
title = {On Herstein's theorems relating modularity in A and A(+).},
url = {http://eudml.org/doc/39953},
volume = {7},
year = {1992},
}

TY - JOUR
AU - Anquela, José A.
TI - On Herstein's theorems relating modularity in A and A(+).
JO - Extracta Mathematicae
PY - 1992
VL - 7
IS - 1
SP - 5
EP - 8
AB - In this paper we will examine the relationship between modularity in the lattices of subalgebras of A and A(+), for A an associative algebra over an algebraically closed field. To this aim we will construct an ideal which measures the modularity of an algebra (not necessarily associative) in paragraph 1, examine modular associative algebras in paragraph 2, and prove in paragraph 3 that the ideal constructed in paragraph 1 coincides for A and A(+). We will also examine some properties of the ideal mentioned in paragraph 1 when the algebras involved are Jordan.
LA - eng
KW - Algebras de Jordan; Estructuras modulares; Retículos; Anillos no conmutativos; Jordan algebra; special Jordan algebra; lattice of subalgebras; modular lattice; radical ideal
UR - http://eudml.org/doc/39953
ER -

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