 -matrix 76
 -homomorphism 75
-isomorphic modules 75
-isomorphism 75
-module 70
-submodule 70
Adjoint of a linear transformation 5
Adjoint of a semilinear transformation 35
Affine transformation 54
Algebra 46
Annihilator 60
Atomic ring 69
Basis 3
Bilinear form 4
Biorthogonal sets 81
Bitranslation 55
Boolean ring 46
Cauchy net 129
Center 45
centralizer 48
Centralizer of a primitive ring 154
Characteristic 16
Circle composition 62
Codimension 119
Complement 3
Complete direct sum 96
Complete lattice 125
Complete uniform space 129
Completely 0-simpla semigroup 71
Completion of a uniform space 129
Congruence (induced by) 54
Conjugate of a linear transformation 6
Conjugate of a semilinear transformation 127
Conjugate space 2
Contains small sets 133
Converges (a net _) 129
Dense extension 54
Dense set of linear transformations 12
Dense uniform subspace 129
Diagonal 128
DIMENSION 3
Direct product of rings 96
Direct product of semigroups 97
Direct sum 91
Directed set 129
Directs (a binary relation_) 129
Discrete direct sum 96
Division ring 1
Doubly transitive 12
Dual pair 4
Dual space 2
Endomorphism 3
Essential extension 60
Eventually in (net _) 129
Extension 54
External direct sum 96
Faithful module 71
Finite intersection property 132
Finite topology of  113
Finite topology of  113
Finite topology of  136
General linear group 29
Generalized inner automorphism 62
Generates (a set _) 81
Generating set 3
Green's relations 75
Homogeneous component 94
Homothetic transformation 54
Hyperplane 115
Ideal 6
Idealizer 11
Idempotent ideal 66
Identity relation 128
In (net _ a set) 129
Independent family of subrings 91
Independent system of primitive ideals 163
Induced by a semilinear isomorphism 41
Induced congruence 54
Inner automorphism 48
Inner bitranslation 55
Inner left (right) translation 55
Inverse limit 156
Inverse system of topological modules 156
Invertible matrix 53
Irreducible module 71
Isomorphic dual pairs 38
Isomorphic vector spaces 34
Jacobson radical 163
Large ideal 60
Left -module 73
Left annihilator 19 66 91
Left ideal 27
Left row-independent matrix 76
Left socle 69
Left socle topology 147 149
Left translation 55
Left vector space 1
Linear form 2
Linear transformation 2
Linear variety 132
Linearly compact module 132
Linearly independent set 3
Linearly topologized module 131
Locally matrix ring 25
| Maximal dense extension 54
Maximal subgroup 25
Minimal left (right, two-sided) ideal 67
Modular left identity 141
Modular right ideal 141
Multiplication induced by a scalar 44
N-fold transitive 12
Natural image 4
Natural isomorphism of V into  26
Net 129
Nilpotent element 74
Nilpotent ideal 66
Nondegenerate bilinear form 4
Null space 3
Open function 126
Order isomorphism 23
Orthogonal set of idempotents 15
Orthogonal sum 92
Pair of dual vector spaces 4
Permutable translations 61
Prime ideal 71
Prime ring 71
Primitive ideal 162
Primitive idempotent 81
Primitive regular semigroup 97
Primitive ring 71
Principal factor 27
Product of relations 75
Product of topological spaces 112
Product topology 113
Projection homomorphism 96
Proper ideal 32
Quasi-inner automorphism 62
R-maximal ring 86
R-maximal semigroup 86
RANGE 3
Rank 3
Rees matrix ring 76
Rees matrix semigroup 29
Rees quotient 27
Regular element (semigroup, ring) 19
Relative uniformity 129
Relativization of a uniformity 129
Ri-semigroup 85
Right annihilator 19 66 91
Right column-independent matrix 76
Right ideal 27
Right K-module 70
Right socle 69
Right socle topology 147 149
Right translation 55
Right vector space 2
Ring of endomorphisms 3
Row finite matrix 52
Sandwich matrix 29
Scalar multiplication 2
Scalars 2
Semidirect product 50
Semigroup 3
Semigroup of endomorphisms 3
Semigroup socle 73
Semilinear automorphism 34
Semilinear isomorphism of dual pairs 38
Semilinear isomorphism of vector spaces 34
Semilinear transformation 34
Semiprime ideal 71
Semiprime ring 66
Semiprime semigroup 67
Semisimple ring 163
Simple ring 19
Socle 68
Split extension 51
Subdirect sum (product) 96
subspace 3
Subvariety 132
Sum of subrings 68
T-subspace 4
Topologica1ly simple ring 162
Topological group 114
Topological module 131
Topological ring 137
Topological vector space 115
Topology of a uniformity 128
Topology of uniform convergence 144
Total subspace 4
Transitive 12
Translation 54
Translationa1 hull 55
U-topology 113
Uniform isomorphism 129
Uniform semigroup (ring) 63
Uniform space 128
Uniform subspace 129
Uniform topology 144
Uniformity 128
Uniformity of uniform convergence 144
Uniformly continuous function 129
Uniformly equivalent uniform spaces 129
Unique addition 45
V-topology 113
Vectors 2
Weakly reductive semigroup 54
Weakly topologized vector space 131
Zero ring 19
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