Definition of a semiring of sets - Mathematics Stack Exchange
2018年10月21日 · I'm reading Halmos's Measure Theory and his definition of semiring seems to disagree with the ones that I find on the internet. Halmos's definition (p. 22): A semiring is a non empty class $\mathbf{P}$ of sets such that
About the definition of a (completely) regular semiring
2019年8月13日 · Shouldn't a regular semiring necessarily satisfy the regularity w.r.t both the operations? Yes, $\mathbb Z$ is a regular semiring in the sense of second definition. But, how do we show its regularity in terms of the first definition? $\endgroup$
Is the ring and semi-ring definition of algebra and set linked?
A semiring in abstract algebra, is an algebraic structure similar to a ring, but without the requirement that each element must have an additive inverse. In Set theory A ring of sets in measure theory is a family of sets closed under unions and set-theoretic differences.
measure theory - How do I prove that every ring is a semiring ...
If a set function on a semiring is finitely additive and continuous at the empty set, then is it necessarily a premeasure (i.e., countably additive)? 1 relative sequential compactness in L1 along with convergence in measure implies convergence in L1
Ideals of a ring/semiring - Mathematics Stack Exchange
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What is a semiring without commutativity requirement for addition?
2016年8月27日 · The 1977 paper by Weiner and Griepentrog uses "semiring" to mean a "left and right distributive seminearring", where what they call a seminearring is almost like Wikipedia's near-semirings, but addition is a semigroup rather than a monoid (so the axiom about absorptivity of 0 is also not imposed). So their "semirings" are like what I asked ...
What is the difference between semiring and hemiring?
2018年4月28日 · An algebraic structure equipped two binary operations is called a semiring if both the binary operations are associative and one of the operations distributes over the other. Hemiring also seems to be similarly defined.
Multiple definitions of Semirings - Mathematics Stack Exchange
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real analysis - Generated semiring - Mathematics Stack Exchange
Since the intersection of semirings is not necessarily semiring (see is-the-intersection-of-an-arbitrary-collection-of-semirings-a-semiring), the usual method that works for rings (etc.) in this case not works. So (a) it can be proved by a different method (b) there is a counterexample.
abstract algebra - About definition of "ordered semi-ring ...
$\begingroup$ @Soviet: Multiplication in a semiring need not be commutative; if you’re working in a semiring in which it is commutative, then of course each of those inequalities implies the other, but if your multiplication is not commutative, they don’t imply each other. $\endgroup$ –