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• W3170742059 abstract "Let R be a commutative ring with identity and let I be a two-generated ideal of R. We denote by SL2(R) the group of 2×2 matrices over R with determinant 1. We study the action of SL2(R) by matrix right-multiplication on V2(I), the set of generating pairs of I. Let Fitt1(I) be the second Fitting ideal of I. Our main result asserts that V2(I)/SL2(R) identifies with a group of units of R/Fitt1(I) via a natural generalization of the determinant if I can be generated by two regular elements. This result is illustrated in several Bass rings for which we also show that SLn(R) acts transitively on Vn(I) for every n>2. As an application, we derive a formula for the number of cusps of a modular group over a quadratic order." @default.
• W3170742059 created "2021-06-22" @default.
• W3170742059 creator A5004647418 @default.
• W3170742059 date "2021-11-01" @default.
• W3170742059 modified "2023-10-01" @default.
• W3170742059 title "Equivalent generating pairs of an ideal of a commutative ring" @default.
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• W3170742059 doi "https://doi.org/10.1016/j.jalgebra.2021.05.014" @default.
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