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Here are some of the basic properties and computations of Tor groups. [4]Tor R 0 (A, B) ≅ A ⊗ R B for any right R-module A and left R-module B.; Tor R i (A, B) = 0 for all i > 0 if either A or B is flat (for example, free) as an R-module.
In elementary algebra, FOIL is a mnemonic for the standard method of multiplying two binomials [1] —hence the method may be referred to as the FOIL method.The word FOIL is an acronym for the four terms of the product:
The commutative diagram used in the proof of the five lemma. In mathematics, and especially in category theory, a commutative diagram is a diagram such that all directed paths in the diagram with the same start and endpoints lead to the same result. [1]
Informally, a field is a set, along with two operations defined on that set: an addition operation written as a + b, and a multiplication operation written as a ⋅ b, both of which behave similarly as they behave for rational numbers and real numbers, including the existence of an additive inverse −a for all elements a, and of a multiplicative inverse b −1 for every nonzero element b.
In mathematics, an algebraic structure or algebraic system [1] consists of a nonempty set A (called the underlying set, carrier set or domain), a collection of operations on A (typically binary operations such as addition and multiplication), and a finite set of identities (known as axioms) that these operations must satisfy.
Mortgage rates stalled an upward rise this week as financial markets adjusted to a second Trump presidency. The average 30-year mortgage rate was essentially unchanged at 6.78% for the week ...