Semiregular, semiperfect and semipotent matrix rings relative to an ideal

Meltem Altun Özarslan

Makale detayları

Semiregular, semiperfect and semipotent matrix rings relative to an ideal

Yazarlar:

Meltem Altun Özarslan

Yayıncı:

Ankara University

Ana Başlıklar:

Mathematical Sciences

Dergi:

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Vol.73 Issue 1, pp.211-221

Belge Tipi:

Makale

Yayın Tarihi:

3/2024

Belge Dili:

İngilizce

Document ID (Org No.):

2001311915

pISSN:

1303-5991

Anahtar kelimeler:

Özet:

 This paper investigates relative ring theoretical properties in the context of formal triangular matrix rings. The first aim is to study the semiregularity of formal triangular matrix rings relative to an ideal. We prove that the formal triangular matrix ring T is T-semiregular if and only if A is I-semiregular, B is K-semiregular and NM for an ideal Tbiglbeginsmallmatrix I  0 N  K endsmallmatrixbigr of Tbiglbeginsmallmatrix A  0 M  B endsmallmatrixbigr. We also discuss the relative semiperfect formal triangular matrix rings in relation to the strong lifting property of ideals. Moreover, we have considered the behavior of relative semipotent and potent property of formal triangular matrix rings. Several examples are provided throughout the paper in order to highlight our results.

 This paper investigates relative ring theoretical properties in the context of formal triangular matrix rings. The first aim is to study the semiregularity of formal triangular matrix rings relative to an ideal. We prove that the formal triangular matrix ring T is T-semiregular if and only if A is I-semiregular, B is K-semiregular and NM for an ideal Tbiglbeginsmallmatrix I  0 N  K endsmallmatrixbigr of Tbiglbeginsmallmatrix A  0 M  B endsmallmatrixbigr. We also discuss the relative semiperfect formal triangular matrix rings in relation to the strong lifting property of ideals. Moreover, we have considered the behavior of relative semipotent and potent property of formal triangular matrix rings. Several examples are provided throughout the paper in order to highlight our results.

 This paper investigates relative ring theoretical properties in the context of formal triangular matrix rings. The first aim is to study the semiregularity of formal triangular matrix rings relative to an ideal. We prove that the formal triangular matrix ring T is T-semiregular if and only if A is I-semiregular, B is K-semiregular and NM for an ideal Tbiglbeginsmallmatrix I  0 N  K endsmallmatrixbigr of Tbiglbeginsmallmatrix A  0 M  B endsmallmatrixbigr. We also discuss the relative semiperfect formal triangular matrix rings in relation to the strong lifting property of ideals. Moreover, we have considered the behavior of relative semipotent and potent property of formal triangular matrix rings. Several examples are provided throughout the paper in order to highlight our results.

 This paper investigates relative ring theoretical properties in the context of formal triangular matrix rings. The first aim is to study the semiregularity of formal triangular matrix rings relative to an ideal. We prove that the formal triangular matrix ring T is T-semiregular if and only if A is I-semiregular, B is K-semiregular and NM for an ideal Tbiglbeginsmallmatrix I  0 N  K endsmallmatrixbigr of Tbiglbeginsmallmatrix A  0 M  B endsmallmatrixbigr. We also discuss the relative semiperfect formal triangular matrix rings in relation to the strong lifting property of ideals. Moreover, we have considered the behavior of relative semipotent and potent property of formal triangular matrix rings. Several examples are provided throughout the paper in order to highlight our results.

Makale detayları

Semiregular, semiperfect and semipotent matrix rings relative to an ideal

Yazarlar:

Meltem Altun Özarslan

Yayıncı:

Ankara University

Ana Başlıklar:

Mathematical Sciences

Dergi:

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Vol.73 Issue 1, pp.211-221

Belge Tipi:

Makale

Yayın Tarihi:

3/2024

Belge Dili:

İngilizce

Document ID (Org No.):

2001311915

pISSN:

1303-5991

Formal triangular matrix ring

strongly lifting ideal

semiregular ring

semiperfect ring

semipotent ring

Sayı

Makale detayları

Semiregular, semiperfect and semipotent matrix rings relative to an ideal

Yazarlar: Meltem Altun Özarslan

Yayıncı: Ankara University

Ana Başlıklar: Mathematical Sciences

Dergi: Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Vol.73 Issue 1, pp.211-221

Belge Tipi: Makale

Yayın Tarihi: 3/2024

Belge Dili: İngilizce

Document ID (Org No.): 2001311915

pISSN: 1303-5991

Formal triangular matrix ring

strongly lifting ideal

semiregular ring

semiperfect ring

semipotent ring

Sayı

Yazarlar:

Meltem Altun Özarslan

Yayıncı:

Ankara University

Ana Başlıklar:

Mathematical Sciences

Dergi:

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Vol.73 Issue 1, pp.211-221

Belge Tipi:

Makale

Yayın Tarihi:

3/2024

Belge Dili:

İngilizce

Document ID (Org No.):

2001311915

pISSN:

1303-5991