Öz
In this study we first show that satisfies two important homological properties, namely Rees short exact sequence an d short five lemma. In addition, by defining inversive semigroup varieties of we prove that strictly inverse semigroup is isomorphic to the spined product of (C)-inversive semigroup and the idempotent semigroup of . Moreover, we give some consequences of the results to make a detailed classification over . It has been recently defined a new semigroup based on Rees matrix and completely 0-simple semigroups. Further, it has been also proved finiteness conditions and the existence of some fundamental properties over .
Anahtar Kelimeler
Rees matrix semigroup completely 0-simple Semigroup spined product
Kaynakça
- Akgüneş N. Some graph parameters on the strong product of monogenic semigroup graphs. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 20 (1): 412-420, (2018).
- Ciric M, Bogdanovic CS. Spined products of some semigroups. Proceedings of the Japan Academy Ser. A, Mathematical Sciences, 69(9): 357-362, (1993).
- Chen Y, Shum KP. Rees short exact sequence of S-systems. Semigroup Forum, 65: 141-148, (2002).
- Clifford AH, Preston GB. The Algebraic Theory of Semigroups, Volume I. American Mathematical Society second edition (1961).
- Howie JM. Fundamentals of Semigroup Theory. Clarendon Press, Oxford (1995).
- Jafari M, Golchin A, Saany HM. Rees short exact sequence and flatness properties. Semigroup Forum, 99: 32–46, (2019).
- Kimura N. The structure of idempotent semigroups I. Pacific Journal of Mathematics, 8(2): 257-275, (1958).
- Luo Y, Fan X, Li X. Regular congruences on an E-inversive semigroup. Semigroup Forum, 76: 107-123, (2008).
- Mitsch H. Introduction to E-inversive semigroups. Semigroups,114-135,(2000).
- Nagy A. Externally commutative semigroups. In: Special Classes of Semigroups. Advances in Mathematics, vol 1. Springer, Boston, MA 2001.
- Ozalan NU, Cevik AS, Karpuz EG. A new semigroup obtained via known ones. Asian-European Journal of Mathematics, 12(6), (2019).
- Yamada M. Strictly inversive semigroups. Bulletin of Shimane University (Natural Science); 13: 128-138, (1963).
- Wazzan SA. New properties over a new type of wreath products on monoids. Advances in Pure Mathematics, 9: 629-636, (2019)
- Wazzan SA. Zappa-Szep products of semigroups. Applied Mathematics, 6: 1047-1068, (2015).
Öz
Bu çalışmada ilk olarak ' nin iki önemli homolojik özelliği, yani Rees kısa tam dizisi ve kısa beşli lemmayı sağladığı gösterilmiştir. Ek olarak, 'nin ters yarı grup çeşitlerini tanımlayarak, kesin olarak ters yarıgrup 'nın (C)-ters yarıgrup ve 'nın idempotent yarıgrubunun (spined) döndürülmüş çarpımına izomorfik olduğu kanıtlanmıştır. Ayrıca, üzerinden ayrıntılı bir sınıflandırma yapmak için bazı sonuçlar verilmiştir. Son zamanlarda Rees matrisine ve tam 0-basit yarı gruplara dayalı yeni bir yarı grup olan tanımlanmıştır. Dahası üzerinde bazı temel özelliklerin ve sonluluk koşullarının varlığı da kanıtlanmıştır.
Anahtar Kelimeler
Rees matris yarıgrup tam basit sıfır yarıgrup döndürülmüş çarpımlar
Kaynakça
- Akgüneş N. Some graph parameters on the strong product of monogenic semigroup graphs. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 20 (1): 412-420, (2018).
- Ciric M, Bogdanovic CS. Spined products of some semigroups. Proceedings of the Japan Academy Ser. A, Mathematical Sciences, 69(9): 357-362, (1993).
- Chen Y, Shum KP. Rees short exact sequence of S-systems. Semigroup Forum, 65: 141-148, (2002).
- Clifford AH, Preston GB. The Algebraic Theory of Semigroups, Volume I. American Mathematical Society second edition (1961).
- Howie JM. Fundamentals of Semigroup Theory. Clarendon Press, Oxford (1995).
- Jafari M, Golchin A, Saany HM. Rees short exact sequence and flatness properties. Semigroup Forum, 99: 32–46, (2019).
- Kimura N. The structure of idempotent semigroups I. Pacific Journal of Mathematics, 8(2): 257-275, (1958).
- Luo Y, Fan X, Li X. Regular congruences on an E-inversive semigroup. Semigroup Forum, 76: 107-123, (2008).
- Mitsch H. Introduction to E-inversive semigroups. Semigroups,114-135,(2000).
- Nagy A. Externally commutative semigroups. In: Special Classes of Semigroups. Advances in Mathematics, vol 1. Springer, Boston, MA 2001.
- Ozalan NU, Cevik AS, Karpuz EG. A new semigroup obtained via known ones. Asian-European Journal of Mathematics, 12(6), (2019).
- Yamada M. Strictly inversive semigroups. Bulletin of Shimane University (Natural Science); 13: 128-138, (1963).
- Wazzan SA. New properties over a new type of wreath products on monoids. Advances in Pure Mathematics, 9: 629-636, (2019)
- Wazzan SA. Zappa-Szep products of semigroups. Applied Mathematics, 6: 1047-1068, (2015).
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Cebir ve Sayı Teorisi |
| Bölüm | Araştırma Makalesi |
| Yazarlar | |
| Erken Görünüm Tarihi | 6 Ocak 2024 |
| Yayımlanma Tarihi | 19 Ocak 2024 |
| Gönderilme Tarihi | 18 Mayıs 2023 |
| Yayımlandığı Sayı | Yıl 2024 Cilt: 26 Sayı: 1 |