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Title: Abstract Algebra

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In this note, for a division ring we denote by the multiplicative group of i.e., is the group of units of Also, we denote by the center of Finally, denotes the conjugacy class of in Question 1. For a division ring and what are the possible values of It turns out that Question 1 is […]

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All rings in this note have identity. Notation. For a ring and a positive integer we define Question. Let be a ring. If is finite for some then must be finite too? Not surprisingly, the answer, as the following example shows, is negative. Example. Let be the finite field of order Let the polynomial ring […]

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Let be a group. We say that is an involution if So an element of a group is an involution if it is equal to its inverse. Now, what if we replace equality with conjugation and ask: which elements of a group are conjugate to their inverses? That is not easy to answer in general […]

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