Power-Associative Algebras in which Every Subalgebra is a Left Ideal
Canadian mathematical bulletin, Tome 13 (1970) no. 2, pp. 239-243
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By an L-algebra we mean a power-associative nonassociative algebra (not necessarily finite-dimensional) over a field F in which every subalgebra generated by a single element is a left ideal. An H-algebra is a power-associative algebra in which every subalgebra is an ideal. The H-algebras were characterized by D. L. Outcalt in [2]. Let Sα be the semigroup with cardinality α such that if x, y ∊ S α then xy = y. Consider the algebra over a field F with basis S α. Such an algebra is an L-algebra that is not an H-algebra unless S α contains only one element. In this paper we will prove that an algebra A over a field F with char. ≠ 2 is an L-algebra if and only if it is either an H-algebra or has a basis S α where α is the dimension of A.
Rodabaugh, D. J. Power-Associative Algebras in which Every Subalgebra is a Left Ideal. Canadian mathematical bulletin, Tome 13 (1970) no. 2, pp. 239-243. doi: 10.4153/CMB-1970-048-5
@article{10_4153_CMB_1970_048_5,
author = {Rodabaugh, D. J.},
title = {Power-Associative {Algebras} in which {Every} {Subalgebra} is a {Left} {Ideal}},
journal = {Canadian mathematical bulletin},
pages = {239--243},
year = {1970},
volume = {13},
number = {2},
doi = {10.4153/CMB-1970-048-5},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1970-048-5/}
}
TY - JOUR AU - Rodabaugh, D. J. TI - Power-Associative Algebras in which Every Subalgebra is a Left Ideal JO - Canadian mathematical bulletin PY - 1970 SP - 239 EP - 243 VL - 13 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1970-048-5/ DO - 10.4153/CMB-1970-048-5 ID - 10_4153_CMB_1970_048_5 ER -
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