THE STRUCTURE OF THE MULTIPLICATIVE GROUP OF THE QUOTIENT RING OF THE RING OF ALGEBRIC INTEGERS Z[sqrt(-6)]
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Abstract
In this paper, we give a detailed description of the multiplicative group structure of the quotient rings of the ring of algebraic integers Z[sqrt(-6)] with respect to powers of prime ideals. As a consequence, we obtain a complete characterization of the unit group of the quotient ring of the ring of algebraic integers Z[sqrt(-6)] for every nonzero ideal. Finally, the paper constructs an illustrative example that demonstrates how the obtained results can be applied in a specific case.
Keywords
ring of algebraic integers, quotient ring, multiplicative group of a quotient ring
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References
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