• Study Resource
  • Explore
    • Arts & Humanities
    • Business
    • Engineering & Technology
    • Foreign Language
    • History
    • Math
    • Science
    • Social Science

    Top subcategories

    • Advanced Math
    • Algebra
    • Basic Math
    • Calculus
    • Geometry
    • Linear Algebra
    • Pre-Algebra
    • Pre-Calculus
    • Statistics And Probability
    • Trigonometry
    • other →

    Top subcategories

    • Astronomy
    • Astrophysics
    • Biology
    • Chemistry
    • Earth Science
    • Environmental Science
    • Health Science
    • Physics
    • other →

    Top subcategories

    • Anthropology
    • Law
    • Political Science
    • Psychology
    • Sociology
    • other →

    Top subcategories

    • Accounting
    • Economics
    • Finance
    • Management
    • other →

    Top subcategories

    • Aerospace Engineering
    • Bioengineering
    • Chemical Engineering
    • Civil Engineering
    • Computer Science
    • Electrical Engineering
    • Industrial Engineering
    • Mechanical Engineering
    • Web Design
    • other →

    Top subcategories

    • Architecture
    • Communications
    • English
    • Gender Studies
    • Music
    • Performing Arts
    • Philosophy
    • Religious Studies
    • Writing
    • other →

    Top subcategories

    • Ancient History
    • European History
    • US History
    • World History
    • other →

    Top subcategories

    • Croatian
    • Czech
    • Finnish
    • Greek
    • Hindi
    • Japanese
    • Korean
    • Persian
    • Swedish
    • Turkish
    • other →
 
Profile Documents Logout
Upload
1 Fields and vector spaces
1 Fields and vector spaces

09 finite fields - Math User Home Pages
09 finite fields - Math User Home Pages

H8
H8

Transcendence Degree and Noether Normalization
Transcendence Degree and Noether Normalization

... exponents is greatest, and thus greater than any other power of ys seen. Thus the relation P(y j ) =  yields a relation Q(z j , ys ) =  which is monic in ys , and we contradict the minimality of s just as before. ...
RW - Homeomorphism in Topological Spaces
RW - Homeomorphism in Topological Spaces

TRANSCENDENCE BASES AND N
TRANSCENDENCE BASES AND N

L6: Almost complex structures To study general symplectic
L6: Almost complex structures To study general symplectic

... Corollary: such an E canonically admits the structure of a complex vector bundle. Hence, it has a first Chern class. This is a “characteristic class”; we assign to each complex vector bundle E → B an element c1(E) ∈ H 2(B; Z) such that c1(f ∗E) = f ∗c1(E) is natural under continuous maps and pullbac ...
2. For each binary operation ∗ defined on a set below, determine
2. For each binary operation ∗ defined on a set below, determine

2009-04-02 - Stony Brook Mathematics
2009-04-02 - Stony Brook Mathematics

Basic Terminology and Results for Rings
Basic Terminology and Results for Rings

... uv ∈ R× since (uv)−1 = v −1 u−1 . The set of units R× is an example of a group (meaning that it is a set with one binary operation, in this case multiplication, which contains 1 and is closed under products and inverses). The second course of this sequence, Algebra II, is devoted to the study of gro ...
File
File

... Variables and Expressions Variable – a symbol used to represent a quantity that can change. Coefficient – the number that is multiplied by the variable in an algebraic expression. Numerical expression – an expression that contains only numbers and operations. Algebraic expression – an expression th ...
Classification of Groups of Order n ≤ 8
Classification of Groups of Order n ≤ 8

1.4 Properties of Algebra
1.4 Properties of Algebra

850 Oberwolfach Report 15 Equivariant Sheaves on Flag Varieties
850 Oberwolfach Report 15 Equivariant Sheaves on Flag Varieties

... perfect derived category Perf(Ext(IC)) that can be described for a more general class of dg algebras (see [Sch08a]). This yields an algebraic description of the category of B-equivariant perverse sheaves on X. • The algebra Ext(IC) is isomorphic to the endomorphism algebra of the B-equivariant hyper ...
Fields - MIT Mathematics
Fields - MIT Mathematics

Two proofs of the infinitude of primes Ben Chastek
Two proofs of the infinitude of primes Ben Chastek

Algebraic proficiency - WALKDEN HIGH MATHS DEPARTMENT
Algebraic proficiency - WALKDEN HIGH MATHS DEPARTMENT

Ringoids (Pre%Talk Notes) By Edward Burkard Question: Consider
Ringoids (Pre%Talk Notes) By Edward Burkard Question: Consider

Ex - Alliance Gertz-Ressler High School
Ex - Alliance Gertz-Ressler High School

... order that the words were written in and copied that for the algebraic expression. They ignored the fact that we need 17 less than the unknown amount, meaning we start with an unknown amount and then take 17 away from it. ...
Lecture 1 Linear Superalgebra
Lecture 1 Linear Superalgebra

... Remark 5.5. The first thing we notice is that in the super category, we only define the Berezinian for invertible transformations. This marks an important difference with the determinant, which is defined in ordinary linear algebra for all endomorphisms of a vector space. We immediately see that it ...
SOLUTIONS TO EXERCISES 1.3, 1.12, 1.14, 1.16 Exercise 1.3: Let
SOLUTIONS TO EXERCISES 1.3, 1.12, 1.14, 1.16 Exercise 1.3: Let

... every nonzero element satisfies the polynomial xm − 1 for some positive integer m. Let n = (1 + 1 + · · · + 1), the n-fold sum of 1. Then either 2 = 0 (hence k has characteristic 2), or there exists m ∈ N such that 2m = 1. Then 2m − 1 = 0; since k has no zero divisors, it must be the case that one o ...
1. Basics 1.1. Definitions. Let C be a symmetric monoidal (∞,2
1. Basics 1.1. Definitions. Let C be a symmetric monoidal (∞,2

3.1 Solutions - NIU Math Department
3.1 Solutions - NIU Math Department

Class number in totally imaginary extensions of totally real function
Class number in totally imaginary extensions of totally real function

... We consider the following groups D = divisors of K, D0 = divisors of degree zero of K, P = principal divisors of K, C = D/P = the group of divisors classes, J = D0 /P = the divisors classes of degree zero and δK = greatest common divisor of {deg P1 , . . . , deg Ps∞ }. Recall that we have an isomorp ...
Computing Galois groups by specialisation
Computing Galois groups by specialisation

< 1 ... 36 37 38 39 40 41 42 43 44 ... 47 >

Homomorphism

In abstract algebra, a homomorphism is a structure-preserving map between two algebraic structures (such as groups, rings, or vector spaces). The word homomorphism comes from the ancient Greek language: ὁμός (homos) meaning ""same"" and μορφή (morphe) meaning ""form"" or ""shape"". Isomorphisms, automorphisms, and endomorphisms are special types of homomorphisms.
  • studyres.com © 2025
  • DMCA
  • Privacy
  • Terms
  • Report