what effect has zero on algebraic patterns?
In abstract algebra, the even integers form various algebraic structures that require the inclusion of zero.
Parity of zero
In abstract algebra, the even integers form various algebraic structures that require the inclusion of zero. 
what is the parity of zero? The quality of an integer being even or odd—is even. who invented the number zero? Indian mathematician Brahmagupta is this number an even or odd number? Even number what is the main reason for it being an even number? Zero is an integer multiple of 2, namely so zero is even. during which year was the mathematician born? 598 CE where was he born? Bhillamāla, Gurjaradesa apart from math, what else interested him? Astronomy what observations did he make ? That the Moon is farther from the Earth than the Sun.
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Parity of zero [SEP] Algebraic patterns
In abstract algebra, the even integers form various algebraic structures that require the inclusion of zero. The fact that the additive identity (zero) is even, together with the evenness of sums and additive inverses of even numbers and the associativity of addition, means that the even integers form a group. Moreover, the group of even integers under addition is a subgroup of the group of all integers; this is an elementary example of the subgroup concept. The earlier observation that the rule "even − even = even" forces 0 to be even is part of a general pattern: any nonempty subset of an additive group that is closed under subtraction must be a subgroup, and in particular, must contain the identity.