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If for some e, the left operation L e is the identity operation, then e is called a left identity. Similarly, if R e = id, then e is a right identity. In ring theory, a subring which is invariant under any left multiplication in a ring is called a left ideal. Similarly, a right multiplication-invariant subring is a right ideal.
It can be proven (theorem 1.27 in [2]) that a right group is isomorphic to the direct product of a right zero semigroup and a group, while a right abelian group [1] is the direct product of a right zero semigroup and an abelian group. Left group [1] [2] and left abelian group [1] are defined in analogous way, by substituting right for left in ...
Furthermore, because many operators are not associative, the order within any single level is usually defined by grouping left to right so that 16/4/4 is interpreted as (16/4)/4 = 1 rather than 16/(4/4) = 16; such operators are referred to as "left associative".
Thereby the orientations "left" and "right" are taken from the standard writing of numbers in a place-value notation, such that a left shift increases and a right shift decreases the value of the number ― if the left digits are read first, this makes up a big-endian orientation. Disregarding the boundary effects at both ends of the register ...
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The two basic types are the arithmetic left shift and the arithmetic right shift. For binary numbers it is a bitwise operation that shifts all of the bits of its operand; every bit in the operand is simply moved a given number of bit positions, and the vacant bit-positions are filled in.
A left-and-right-truncatable prime is a prime which remains prime if the leading ("left") and last ("right") digits are simultaneously successively removed down to a one- or two-digit prime. 1825711 is an example of a left-and-right-truncatable prime, since 1825711, 82571, 257, and 5 are all prime.
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