Eléna Wexler-Kreindler

Born: 15 October 1931 in Brăila, Romania
Died: August 1992 in Paris, France

Eléna Kreindler (perhaps better known by the name she adopted after her marriage Eléna Wexler-Kreindler) was the daughter of Oscar Kreindler, a professor of mathematics at the Polytechnic in Brăila. The family was Jewish. Eléna studied at the high school in Bucharest, graduating in 1951. The quality of her work was outstanding and it led to her being awarded a fellowship to finace her university studies at the University of Sverdlovsk (now Ekaterinburg or Yekaterinburg in Russia). There she studied with P G Kantorovich and under his supervision she wrote an M.Sc. thesis Multiplicative lattices with additive basis.

Returning from Ekaterinburg to Bucharest, Kreindler was appointed as an instructor at the Polytechnic Institute. Her first publication was On principal ideals of lattices (1960). Here is her own description of the contents of this paper:-

We propose to study the lattice L ideals of an algebraic system S, which satisfies the finite chain condition, in particular of an arbitrary lattice. It is known that the principal ideals of a lattice S form a sublattice L' of the lattice L of all its ideals. In the case of a lattice S of finite length L and L' coincide. Using the additive basis method, we characterize the class of the lattices S for which L and L' coincide. In particular we obtain for rings a result similar to that known in the theory of groups.
Kreindler's career developed and she was promoted to assistant professor at the Polytechnic Institute. Despite a heavy teaching load, she vigorously pursued her research. Further papers included Sur un opérateur de dérivation dans les modules unitaires et dans les espaces vectoriels (1965), Opérateurs additifs dans les modules unitaires à base dénombrable (1965), and Le module des combinaisons différentielles linéaires à coefficients variables (1966). For her work on functional analysis, carried out with G C Moisil as her supervisor, she was awarded a doctorate having submitted her thesis Theory of Pseudolinear operators. In 1969 she was promoted to associate professor.

Kreindler marred Dinu Wexler who was a fellow mathematician and at this time she changed her name to Eléna Wexler-Kreindler. The two mathematicians left Bucharest in 1972 and Eléna had to begin her career again. She continued to publish with Catégories abéliennes avec objets principaux appearing in 1973. This paper, written now under the name Wexler-Kreindler, is described by her as follows:-

The object of this note is to include in the language of the theory of abelian categories some results known in the theory of modules over principal rings, in particular the theorem concerning the submodules of free modules over principal rings, as well as the theorem on the invariants factors of a submodule of finite type of a free module over a principal ring (non-commutative).
The overview of her research in France is given in [1]:-
Her own research interests in Paris focused on some difficult problems in modern algebra, such as Ore's extensions, the theory of filtered rings, or algebraic microlocalisation. She participated actively in both Mrs M-P Malliavin's regular algebra seminar and in the Lesieur-Renault seminar on noncommutative algebra. Most of these results were also presented in international workshops and conferences, and published in various scientific journals.
To give a single example let us mention her paper Anneaux filtrés complets et suites spectrales associées (1982) which Wexler-Kreindler summarises as follows:-
We study certain homological properties of complete filtered rings by means that are closely related to their structure. This allows us to extend some of J E Björk's results [in Rings of differential operators (1979)] to other, non-Noetherian filtered rings as well as to filtered modules that are not of finite type.
On settling in Paris she worked first as an untenured assistant professor but eventually was appointed to a tenured position at the Pierre & Marie Curie University Paris VI. She was promoted to associate professor in 1989, the year in which her husband Dinu Wexler died. In the following year she was granted the right to supervise graduate students but sadly she died in 1992 at the age of 60.

Her qualities as a teacher are emphasised in [1]:-

... Eléna Wexler-Kreindler was an outstanding lecturer and had a great passion for teaching both graduate and undergraduate mathematics. She was always generous towards students with her time and devoted herself to making even the harshest matter accessible to the audience. Her lecture notes and collections of solved problems will remain a model of clarity and self-consistency.
Since this quote emphasises her "collections of solved problems" we should mention that she published in collaboration with Marie José Bertin, Algèbre commutative: exercices. Applications en géométrie et théorie des nombres which is a companion volume to the text Algèbre commutative by M-P Malliavin.

Article by: J J O'Connor and E F Robertson

July 2007
MacTutor History of Mathematics