Inner automorphisms of Clifford monoids

Aftab Shah; Thomas Quinn-gregson

Makale detayları

Inner automorphisms of Clifford monoids

Yazarlar:

Aftab Shah | Thomas Quinn-gregson

Yayıncı:

Hacettepe University

Ana Başlıklar:

Mathematical Sciences

Dergi:

Hacettepe Journal of Mathematics and Statistics Vol.53 Issue 4, pp.1060-1074

Belge Tipi:

Makale

Yayın Tarihi:

8/2024

Belge Dili:

İngilizce

Document ID (Org No.):

2001325556

pISSN:

2651-477X

Anahtar kelimeler:

Özet:

 An automorphism phi of a monoid S is called inner if there exists g in U_S, the group of units of S, such that phisgsg-1 for all s  in S; we call S nearly complete if all of its automorphisms are inner. In this paper, first we prove several results on inner automorphisms of a general monoid and subsequently apply them to Clifford monoids. For certain subclasses of the class of Clifford monoids, we give necessary and sufficient conditions for a Clifford monoid to be nearly complete. These subclasses arise from conditions on the structure homomorphisms of the Clifford monoids: all being either bijective, surjective, injective, or image trivial.

 An automorphism phi of a monoid S is called inner if there exists g in U_S, the group of units of S, such that phisgsg-1 for all s  in S; we call S nearly complete if all of its automorphisms are inner. In this paper, first we prove several results on inner automorphisms of a general monoid and subsequently apply them to Clifford monoids. For certain subclasses of the class of Clifford monoids, we give necessary and sufficient conditions for a Clifford monoid to be nearly complete. These subclasses arise from conditions on the structure homomorphisms of the Clifford monoids: all being either bijective, surjective, injective, or image trivial.

 An automorphism phi of a monoid S is called inner if there exists g in U_S, the group of units of S, such that phisgsg-1 for all s  in S; we call S nearly complete if all of its automorphisms are inner. In this paper, first we prove several results on inner automorphisms of a general monoid and subsequently apply them to Clifford monoids. For certain subclasses of the class of Clifford monoids, we give necessary and sufficient conditions for a Clifford monoid to be nearly complete. These subclasses arise from conditions on the structure homomorphisms of the Clifford monoids: all being either bijective, surjective, injective, or image trivial.

 An automorphism phi of a monoid S is called inner if there exists g in U_S, the group of units of S, such that phisgsg-1 for all s  in S; we call S nearly complete if all of its automorphisms are inner. In this paper, first we prove several results on inner automorphisms of a general monoid and subsequently apply them to Clifford monoids. For certain subclasses of the class of Clifford monoids, we give necessary and sufficient conditions for a Clifford monoid to be nearly complete. These subclasses arise from conditions on the structure homomorphisms of the Clifford monoids: all being either bijective, surjective, injective, or image trivial.

Makale detayları

Inner automorphisms of Clifford monoids

Yazarlar:

Aftab Shah | Thomas Quinn-gregson

Yayıncı:

Hacettepe University

Ana Başlıklar:

Mathematical Sciences

Dergi:

Hacettepe Journal of Mathematics and Statistics Vol.53 Issue 4, pp.1060-1074

Belge Tipi:

Makale

Yayın Tarihi:

8/2024

Belge Dili:

İngilizce

Document ID (Org No.):

2001325556

pISSN:

2651-477X

idempotents

center

nearly complete

inner automorphisms

structure homomorphisms

semilattice of groups

Sayı

Makale detayları

Inner automorphisms of Clifford monoids

Yazarlar: Aftab Shah | Thomas Quinn-gregson

Yayıncı: Hacettepe University

Ana Başlıklar: Mathematical Sciences

Dergi: Hacettepe Journal of Mathematics and Statistics Vol.53 Issue 4, pp.1060-1074

Belge Tipi: Makale

Yayın Tarihi: 8/2024

Belge Dili: İngilizce

Document ID (Org No.): 2001325556

pISSN: 2651-477X

idempotents

center

nearly complete

inner automorphisms

structure homomorphisms

semilattice of groups

Sayı

Yazarlar:

Aftab Shah | Thomas Quinn-gregson

Yayıncı:

Hacettepe University

Ana Başlıklar:

Mathematical Sciences

Dergi:

Hacettepe Journal of Mathematics and Statistics Vol.53 Issue 4, pp.1060-1074

Belge Tipi:

Makale

Yayın Tarihi:

8/2024

Belge Dili:

İngilizce

Document ID (Org No.):

2001325556

pISSN:

2651-477X