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Let S be a commutative semiring and A,B [member of] [M.sub.m,n](S).
We say that a left regular band B is geometric if, for each a [member of] B, the left stabilizer {b [member of] B | b [[less than or equal to].sub.R] a} of a is commutative (and hence a lattice under the order [[less than or equal to].sub.R] with the meet given by the product).
Livingston, "The zero-divisor graph of a commutative ring," Journal of Algebra, vol.
We think students taking a course in commutative algebra and algebraic geometry should be equipped to do computations in the area, hence, Grobner bases need to be covered.
Then there are induced fuzzy deformation retract, fuzzy retraction, and the limit of the fuzzy foldings such that the following diagram is commutative.
What constitutes commutative justice in Hume, Smith, and classical liberalism generally is property, consent, and contract.
This approach to learning mathematics led children to a deeper understanding of the meaning of multiplication and its connection to other mathematical ideas, such as the commutative property and its inverse operation.
We prove that A and G/[C.sub.G] (A) are commutative groups.
Then (P(t), [[tau].sub.c]) is a commutative unital locally convex (not normed) TQ-algebras (see [12], Example 2).
Let R be a commutative semiring and A a cyclic R-semimodule.
Let R be a prime ring of char R [not equal to] 2 and d a non-zero derivation of R and 0 [not equal to] b [member of] R such that b[[[d(x), x].sub.n], [[y, d(y)].sub.m]] = 0 for all x, y [member of] R, where n,m [greater than or equal to] 0 are fixed integers, then R is commutative.
We observe that, when N is a commutative near-ring, the concepts of strong [S.sub.1] and strong [S.sub.2] near-rings coincide.