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  2. Luhn algorithm - Wikipedia

    en.wikipedia.org/wiki/Luhn_algorithm

    The Luhn mod N algorithm is an extension that supports non-numerical strings. Because the algorithm operates on the digits in a right-to-left manner and zero digits affect the result only if they cause shift in position, zero-padding the beginning of a string of numbers does not affect the calculation.

  3. Ideal (ring theory) - Wikipedia

    en.wikipedia.org/wiki/Ideal_(ring_theory)

    Ideal correspondence: Given a surjective ring homomorphism ⁠: ⁠, there is a bijective order-preserving correspondence between the left (resp. right, two-sided) ideals of containing the kernel of and the left (resp. right, two-sided) ideals of : the correspondence is given by () and the pre-image ⁠ ⁠.

  4. Category of modules - Wikipedia

    en.wikipedia.org/wiki/Category_of_modules

    The category of right modules is defined in a similar way. One can also define the category of bimodules over a ring R but that category is equivalent to the category of left (or right) modules over the enveloping algebra of R (or over the opposite of that). Note: Some authors use the term module category for the category of modules.

  5. Blum Blum Shub - Wikipedia

    en.wikipedia.org/wiki/Blum_Blum_Shub

    Blum Blum Shub (B.B.S.) is a pseudorandom number generator proposed in 1986 by Lenore Blum, Manuel Blum and Michael Shub [1] that is derived from Michael O. Rabin 's one-way function. Blum Blum Shub takes the form. where M = pq is the product of two large primes p and q. At each step of the algorithm, some output is derived from xn+1; the ...

  6. Quasi-Frobenius ring - Wikipedia

    en.wikipedia.org/wiki/Quasi-Frobenius_ring

    R is right self-injective and a right Kasch ring. R is right self-injective, semilocal and the socle soc(R R) is an essential submodule of R. R is a cogenerator of Mod-R and is a left Kasch ring. A ring R is right finitely pseudo-Frobenius if and only if every finitely generated faithful right R module is a generator of Mod-R.

  7. Simple module - Wikipedia

    en.wikipedia.org/wiki/Simple_module

    Simple module. In mathematics, specifically in ring theory, the simple modules over a ring R are the (left or right) modules over R that are non-zero and have no non-zero proper submodules. Equivalently, a module M is simple if and only if every cyclic submodule generated by a non-zero element of M equals M. Simple modules form building blocks ...

  8. Multiply-with-carry pseudorandom number generator - Wikipedia

    en.wikipedia.org/wiki/Multiply-with-carry...

    Thus, a multiply-with-carry generator is a Lehmer generator with modulus p and multiplier b−1 (mod p ). This is the same as a generator with multiplier b, but producing output in reverse order, which does not affect the quality of the resultant pseudorandom numbers.

  9. Ship of Harkinian - Wikipedia

    en.wikipedia.org/wiki/Ship_of_Harkinian

    www.shipofharkinian.com. Ship of Harkinian is an unofficial source port of the 1998 Nintendo 64 video game, The Legend of Zelda: Ocarina of Time, that runs on Microsoft Windows, Linux, macOS, Wii U, and Nintendo Switch. It first released in March 2022 for Windows, four months after Ocarina of Time 's source code was decompiled and released.