## Index of Memorial Resolutions and Biographical Sketches

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IN MEMORIAM

EFRAIM P. ARMENDARIZ

Efraim P. Armendariz had a lively intelligence, a strong moral sense, a good heart, an astonishing memory, and a passion for mathematics, teaching, and music. He was beloved by family and friends, and he was a great asset to The University of Texas at Austin, where he served as a faculty member from fall 1966 through mid-spring of 2013.

Personal: Efraim was devoted to his wife Edna, to whom he was married for fifty-one years. He was also devoted to his children, Lisa and Paul, and to the many brothers and sisters in his extended family. There was much visiting within this large family and also much music. Efraim played a number of instruments but his favorite was the guitar. With other members of the mathematics department and some members of the extended family, he formed a music group that met for dinner and singing many times over the years. In addition, he played electric guitar in two bands, the blues and rock band Ax Nelson and the Tejano-Latin band Sister Sister y Los Misters. Efraim also enjoyed sports and coached little league baseball for many years.

Teaching: This was high on Efraim’s list of priorities. Over the years, he had an important influence on teaching at UT Austin. He was an active supporter of the UTeach program, focused on the preparation of high school mathematics and science teachers. He was a member of the Mathematical Association of America’s ad hoc committee on a national center for the teaching of undergraduates. He was instrumental in bringing to UT Austin the Emerging Scholars Program initiated at the University of California at Berkeley by Uri Treisman who later joined the UT Austin mathematics department. And he was a dedicated teacher in his own right. The Texas section of the Mathematical Association of America honored him with their 1998 Distinguished Teaching Award.

Administration: Starting in September 1976, Efraim served as the director of the Center for Mexican-American Studies for a little over a year. In 1984, he became the associate chairman of the mathematics department and served for seven years in that capacity. In 1991, he became chairman of the department. At the end of his four-year term as chairman, members of the department asked him to serve for another term, and he agreed. This happened two more times, so that in the end he served as chairman for an astonishing sixteen years. His constant reappointment shows the respect in which he was held by his colleagues and the quality of the work he was doing. And his willingness to serve this long shows the strength of his commitment to the department and the University of Texas. During his chairmanship, he fostered the teaching initiatives mentioned above and vigorously applied himself to the hiring of superb mathematicians who would enhance the mathematical atmosphere in the department and increase its national standing. By the end of his tenure, the department was ranked fourteenth among all United States mathematics departments and fourth among mathematics departments at public universities in the United States.

Research: Efraim was a specialist in noncommutative ring theory, a basic area of twentieth-century algebra. Frequently, he and his collaborators would adopt the point of view that commutative rings and finite-dimensional algebras were more amenable to analysis, and then they tried to understand to what extent general noncommutative rings could be understood based on these more tractable cases. This led Efraim to study so-called P.I. rings, which, it was hoped, behaved like commutative rings. Efraim was particularly known for studying P.I. rings that satisfied von Neumann regularity and similar properties. Here, Efraim and his coauthors proved striking results detailing how precisely worded statements could be generalized from the commutative case. In another direction, Efraim noticed that so-called reduced rings had an interesting property connected to polynomials and rings with this property came to be called Armendariz rings. Various authors studied and are continuing to study Armendariz rings and related concepts.

Postscript: By way of illustrating the astonishing memory that stood Efraim in such good stead in his various administrative positions: when he was having dinner in his first year in the Corps at Texas A&M University, an upper classman said if he wanted dessert, he would have to name the third book from the left on the second shelf of the bookcase just inside the door of the library. Efraim got his dessert.

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William Powers Jr., President

The University of Texas at Austin

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Sue Alexander Greninger, Secretary

The General Faculty

This memorial resolution was prepared by a special committee consisting of Professors John D. Dollard (chair), David J. Saltman, and Cameron M. Gordon.