Inductive groupoids and normal categories of regular semigroups
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Arangath Raghavan Rajan
Abstract
Inductive groupoids and normal categories arise in the structure theory of regular semigroups. Inductive groupoid of a regular semigroup S is the groupoid G(S){(x, xı) : xı is an inverse of x} which admits certain order structure. Normal category is an abstraction of the structure in the category of principal left [or right] ideals of a regular semigroup with translations as morphisms. Here we show that an inductive groupoid G(C) arises from every normal category C. In the case when S is a regular semigroup the inductive groupoids G(S) and G(C) where C is the normal category of principal left ideals of S are closely related.We provide explicit desciption of this relation
Abstract
Inductive groupoids and normal categories arise in the structure theory of regular semigroups. Inductive groupoid of a regular semigroup S is the groupoid G(S){(x, xı) : xı is an inverse of x} which admits certain order structure. Normal category is an abstraction of the structure in the category of principal left [or right] ideals of a regular semigroup with translations as morphisms. Here we show that an inductive groupoid G(C) arises from every normal category C. In the case when S is a regular semigroup the inductive groupoids G(S) and G(C) where C is the normal category of principal left ideals of S are closely related.We provide explicit desciption of this relation
Kapitel in diesem Buch
- Frontmatter I
- Preface V
- Contents VII
- On structure of ∗-prime rings with generalized derivation 1
- A characterization of additive mappings in rings with involution 11
- Skew constacyclic codes over Fq + vFq + v2Fq 25
- Generalized total graphs of commutative rings: a survey 37
- Differential conditions for which near-rings are commutative rings 55
- Generalized skew derivations satisfying the second posner’s theorem on lie ideals 65
- Generalized skew-derivations on lie ideals in prime rings 81
- On generalized derivations and commutativity of prime rings with involution 91
- On (n, d)-krull property in amalgamated algebra 101
- Pure ideals in ordered Γ-semigroups 111
- Projective ideals of differential polynomial rings over hnp rings 121
- Additive central m-power skew-commuting maps on semiprime rings 135
- A note on cess-lattices 151
- Properties inherited by direct sums of copies of a module 163
- Modules witnessing that a leavitt path algebra is directly infinite 181
- Inductive groupoids and normal categories of regular semigroups 193
- Actions of generalized derivations in rings and banach algebras 201
- Proper categories and their duals 215
- On nakayama conjecture and related conjectures-review 227
- On construction of global actions for partial actions 243
- On 2-absorbing and weakly 2-absorbing ideals in product lattices 253
- Separability in algebra and category theory 265
- Annihilators of power values of generalized skew derivations on lie ideals 307
- Generalized derivations on prime rings with involution 317
Kapitel in diesem Buch
- Frontmatter I
- Preface V
- Contents VII
- On structure of ∗-prime rings with generalized derivation 1
- A characterization of additive mappings in rings with involution 11
- Skew constacyclic codes over Fq + vFq + v2Fq 25
- Generalized total graphs of commutative rings: a survey 37
- Differential conditions for which near-rings are commutative rings 55
- Generalized skew derivations satisfying the second posner’s theorem on lie ideals 65
- Generalized skew-derivations on lie ideals in prime rings 81
- On generalized derivations and commutativity of prime rings with involution 91
- On (n, d)-krull property in amalgamated algebra 101
- Pure ideals in ordered Γ-semigroups 111
- Projective ideals of differential polynomial rings over hnp rings 121
- Additive central m-power skew-commuting maps on semiprime rings 135
- A note on cess-lattices 151
- Properties inherited by direct sums of copies of a module 163
- Modules witnessing that a leavitt path algebra is directly infinite 181
- Inductive groupoids and normal categories of regular semigroups 193
- Actions of generalized derivations in rings and banach algebras 201
- Proper categories and their duals 215
- On nakayama conjecture and related conjectures-review 227
- On construction of global actions for partial actions 243
- On 2-absorbing and weakly 2-absorbing ideals in product lattices 253
- Separability in algebra and category theory 265
- Annihilators of power values of generalized skew derivations on lie ideals 307
- Generalized derivations on prime rings with involution 317
