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The free monoid on a set A is usually denoted A ∗. The free semigroup on A is the subsemigroup of A ∗ containing all elements except the empty string. It is usually denoted A +. [1] [2] More generally, an abstract monoid (or semigroup) S is described as free if it is isomorphic to the free monoid (or semigroup) on some set. [3]
In addition, corporations may change key aspects of their legal identity, capitalization, or structure in a tax free manner. Examples of reorganizations that may be tax free include mergers, liquidations of subsidiaries, share for share exchanges, exchanges of shares for assets, changes in form or place of organization, and recapitalizations. [60]
An S corporation (or S Corp), for United States federal income tax, is a closely held corporation (or, in some cases, a limited liability company (LLC) or a partnership) that makes a valid election to be taxed under Subchapter S of Chapter 1 of the Internal Revenue Code. [1] In general, S corporations do not pay any income taxes.
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The Kleene star is defined for any monoid, not just strings. More precisely, let (M, ⋅) be a monoid, and S ⊆ M. Then S * is the smallest submonoid of M containing S; that is, S * contains the neutral element of M, the set S, and is such that if x,y ∈ S *, then x⋅y ∈ S *.
The monoid is then presented as the quotient of the free monoid (or the free semigroup) by these relations. This is an analogue of a group presentation in group theory. As a mathematical structure, a monoid presentation is identical to a string rewriting system (also known as a semi-Thue system). Every monoid may be presented by a semi-Thue ...
Corporate tax rates generally are the same for differing types of income, yet the US graduated its tax rate system where corporations with lower levels of income pay a lower rate of tax, with rates varying from 15% on the first $50,000 of income to 35% on incomes over $10,000,000, with phase-outs.
“For example, let’s say a direct indexing account was able to harvest tax losses of $100,000. If we assume a maximum long-term capital gains tax of 23.8%, the tax savings would be $23,800.
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