In abstract algebra, an element a of a ring R is called a left zero divisor if there exists a nonzero x in R such that ax = 0, or equivalently if the map...

divisors are a generalization of codimension-1 subvarieties of algebraic varieties. Two different generalizations are in common use, Cartier divisors...

the zero-product property".) Equivalently, a domain is a ring in which 0 is the only left zero divisor (or equivalently, the only right zero divisor). A...

in combinatorial commutative algebra, a zero-divisor graph is an undirected graph representing the zero divisors of a commutative ring. It has elements...

set up divisor (13) for second division loop (MEMORY LAYOUT: zero copy dividend divisor remainder quotient zero zero) >-[>+>>] Reduce divisor; Normal...

the greatest common divisor (GCD), also known as greatest common factor (GCF), of two or more integers, which are not all zero, is the largest positive...

division algebra because they have zero divisors. This means that two nonzero sedenions can be multiplied to obtain zero: an example is ( e 3 + e 10 ) (...

In mathematics, division by zero, division where the divisor (denominator) is zero, is a unique and problematic special case. Using fraction notation,...

rule of zero product, the null factor law, the multiplication property of zero, the nonexistence of nontrivial zero divisors, or one of the two zero-factor...

trivial group {0}. The element 0 in the zero ring is not a zero divisor. The only ideal in the zero ring is the zero ideal {0}, which is also the unit ideal...

terminology by making an exception for zero divisors: one calls an element a in a commutative ring a zero divisor if there exists a nonzero x such that...

z} of a Banach algebra A {\displaystyle A} is called a topological divisor of zero if there exists a sequence x 1 , x 2 , x 3 , . . . {\displaystyle x_{1}...

In mathematics, a divisor of an integer n , {\displaystyle n,} also called a factor of n , {\displaystyle n,} is an integer m {\displaystyle m} that may...

algebra and f a homogeneous element of degree d in A which is not a zero divisor. Then we have H S A / ( f ) ( t ) = ( 1 − t d ) H S A ( t ) . {\displaystyle...

is either 0 or a zero divisor. Thus in rings where zero divisors do not exist, it is uniquely 0. However, rings with zero divisors may have multiple...

nonzero element has a multiplicative inverse, but which nonetheless has divisors of zero, that is, nonzero elements x, y such that xy = 0. A square matrix has...

additive identity among those tensors. Null semigroup Zero divisor Zero object Zero of a function Zero — non-mathematical uses Nair, M. Thamban; Singh, Arindama...

commutative rings R that may have zero divisors. The construction embeds R in a larger ring, giving every non-zero-divisor of R an inverse in the larger ring...

left zero divisor of a ring R is an element a in the ring such that there exists a nonzero element b of R such that ab = 0. A right zero divisor is defined...

What is being divided is called the dividend, which is divided by the divisor, and the result is called the quotient. At an elementary level the division...

torsion element is an element of a module that yields zero when multiplied by some non-zero-divisor of the ring. The torsion submodule of a module is the...

amazônicas do Brasil: saúde e história social. Marco Zero. p. 181. ISBN 852790313X. "Sierra del Divisor | Huge Amazon National Park | Pucallpa, Ucayali &...

theory, a nonzero element of a ring that is neither a left nor a right zero divisor In ring theory, a von Neumann regular element of a ring A regular element...

module is a module over a ring such that zero is the only element annihilated by a regular element (non zero-divisor) of the ring. In other words, a module...

The Zero Divisor Theorem. If M ≠ 0 {\displaystyle M\neq 0} has finite projective dimension and r ∈ R {\displaystyle r\in R} is not a zero divisor on M...

torsion-free group. Kaplansky's zero divisor conjecture states: The group ring K[G] does not contain nontrivial zero divisors, that is, it is a domain. Two...

element r of R is a called a two-sided zero divisor if it is both a left zero divisor and a right zero divisor. division A division ring or skew field...

{\displaystyle s\in S,} and 0 ≠ a ∈ R {\displaystyle 0\neq a\in R} is a zero divisor with a s = 0. {\displaystyle as=0.} Then a 1 {\displaystyle {\tfrac {a}{1}}}...

only if every zero divisor in R/Q is nilpotent. (Compare this to the case of prime ideals, where P is prime if and only if every zero divisor in R/P is actually...

that 0 is the only element annihilated by a regular element (non zero-divisor) of the ring, equivalently rm = 0 implies r = 0 or m = 0. Noetherian A...