A walk through the loop rings
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Universidad Industrial de Santander
Abstract
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La teoría de anillos de bucles no es solamente una generalización de los anillos de grupos: es una teoría en sí misma, con origen y aún en movimiento. El concepto de anillo de bucles surge en 1944 en los trabajos de R.H. Bruck con la construcción de anillos no asociativos. En los últimos años esta teoría se desarrolló ampliamente. Como ejemplo de esto tenemos la descripción completa del bucle de los elementos invertibles del Álgebra de Zorn. En este trabajo se hace un recorrido a lo largo del desarrollo de esta teoría que ha intrigado a matemáticos de diversas áreas.
The loop ring theory is more that a generalization of group rings; in fact, it is a theory with its own spirit, with origin and still in development. The loop rings borns in 1944 with the works of R. H. Bruck about construction of non-associative rings. In recent years, this theory was developed largely, and as an example of this we know now the complete description of the loop of invertible elements of the Zorn algebra. In this paper we travel through the development of this theory that has intrigued mathematicians from different areas.
The loop ring theory is more that a generalization of group rings; in fact, it is a theory with its own spirit, with origin and still in development. The loop rings borns in 1944 with the works of R. H. Bruck about construction of non-associative rings. In recent years, this theory was developed largely, and as an example of this we know now the complete description of the loop of invertible elements of the Zorn algebra. In this paper we travel through the development of this theory that has intrigued mathematicians from different areas.
Keywords
quasigroup, loops, Moufang, alternative ring, loop rings, cuasigrupos, bucles, Moufang, anillos alternantes, anillos de bucles