Let M be a monoid and let θ be an endomorphism on M. Then the set N^0×M×N^0 where N^0 is the set of non-negative integers, is a monoid together with the binary operation
where r=max{n,p} and θ^0 is the identity map on M, which is called the Bruck-Reilly extension of M determined by θ and denoted by BR(M,θ). In this paper, we show that the second integral homology of Bruck-Reilly extension of a finite monoid M is
Araujo, I.M. and Ruskuc, N., 2001. Finite presentability of Bruck-Reilly extensions of groups. J. Algebra, 242(1), 20-30.
Ayık, H., Campbell, C.M., O’Connor, J.J. and Ruskuc, N., 2000. Minimal presentations and efficiency of semigroups. Semigroup Forum, 60, 231-242.
Ayık, H., Campbell, C.M., O’Connor, J.J. and Ruskuc, N., 2000. On the efficiency of finite simple semigroups. Turk J. Math, 24, 129-146.
Ayık, H., Campbell, C.M., O’Connor, J.J. and Ruskuc, N., 2000. The semigroup efficiency of groups and monoids. Mathematical Proceedings of the Royal Irish Academy, 100A(2), 171-176.
Ayık, H., Campbell, C.M. and O’Connor, J.J., 2007. On the efficiency of the direct products of Monogenic Monoids. Algebra Colloq., 14, 279-284.
Bruck, R. H., 1958. A Survey of Binary Systems, Ergebnisse der Mathematik und ihrer Grenzgebiete, Neue Folge, Heft 20. Reihe: Gruppentheorie, Springer, Berlin.
Bugay, L., 2010. Yarıgrupların Bruck-Reilly genişlemelerinin sonlu takdim edilebilirliği. Yüksek Lisans Tezi, Çukurova Üniversitesi Fen Bilimleri Enstitüsü, Adana, 109.
Carvalho, C.A., 2005. On Bruck-Reilly extensions of rectangular bands, zero semigroups and free monoids. Southeast Asian Bull. Math., 29(3), 423-431.
Carvalho, C.A. and Ruskuc, N, 2006. Finite presentability of Bruck-Reilly extensions of semilattices. Communications in Algebra, 34(9), 3301-3313.
Carvalho, C.A. and Ruskuc, N, 2007. Finite presentability of Bruck-Reilly extensions of Clifford monoids. Journal of Algebra and Its Applications, 6(5), 801-814.
Carvalho, C.A., 2009. Bruck-Reilly extensions of direct products of monoids and completely (0)-simple semigroups. Semigroup Forum, 79, 145-158.
Carvalho, C.A., 2009. On Presentations of Bruck-Reilly extensions. Communications in Algebra, 34, 2871-2886.
Çevik, A.S, 2003. Minimal but inefficient presentations of the semi-direct products of some monoids. Semigroup Forum, 66, 1-17.
Çevik, A.S, 2003. The p-Cockcroft propertyof the semi-direct products of monoids. Internat. J. Algebra Comput., 13, 1-16.
Guba, V.S. and Pride, S.J., 1996. Low dimensional (co)homology of free Burnside monoids. Journal Pure Appl. Algebra, 108, 61-79.
Howie, J. M. and Ruskuc, N., 1994. Construction and presentations for monnoids. Communications in Algebra, 22(15), 6209-6224.
Howie, J. M., 1995. Fundamentals of Semigroup Theory. New York, Oxford University Press.
Johnson, D.L., 1990. Presentations of Groups. Cambridge Univ. Press, Cambridge.
Karpuz, E. G., 2015. Gröbner-Shirshov Bases of Some Semigroup Constructions. Algebra Colloquium, 22(1), 35-46.
M bir monoid ve θ, M üzerinde bir endomorfizm olsun. N^0 negatif olmayan tamsayıların kümesi, r=max{n,p} ve θ^0, M üzerinde birim dönüşüm olmak üzere N^0×M×N^0 kümesi
ikili işlemi ile birlikte bir monoid tanımlar. Bu monoide θ nin belirlediği M nin Bruck-Reilly genişlemesi denir ve BR(M,θ) ile gösterilir. Bu çalışmada, bir sonlu M monoidinin Bruck-Reilly genişlemesinin ikinci tamsayı homolojisinin, öyle bir k∈N için
Araujo, I.M. and Ruskuc, N., 2001. Finite presentability of Bruck-Reilly extensions of groups. J. Algebra, 242(1), 20-30.
Ayık, H., Campbell, C.M., O’Connor, J.J. and Ruskuc, N., 2000. Minimal presentations and efficiency of semigroups. Semigroup Forum, 60, 231-242.
Ayık, H., Campbell, C.M., O’Connor, J.J. and Ruskuc, N., 2000. On the efficiency of finite simple semigroups. Turk J. Math, 24, 129-146.
Ayık, H., Campbell, C.M., O’Connor, J.J. and Ruskuc, N., 2000. The semigroup efficiency of groups and monoids. Mathematical Proceedings of the Royal Irish Academy, 100A(2), 171-176.
Ayık, H., Campbell, C.M. and O’Connor, J.J., 2007. On the efficiency of the direct products of Monogenic Monoids. Algebra Colloq., 14, 279-284.
Bruck, R. H., 1958. A Survey of Binary Systems, Ergebnisse der Mathematik und ihrer Grenzgebiete, Neue Folge, Heft 20. Reihe: Gruppentheorie, Springer, Berlin.
Bugay, L., 2010. Yarıgrupların Bruck-Reilly genişlemelerinin sonlu takdim edilebilirliği. Yüksek Lisans Tezi, Çukurova Üniversitesi Fen Bilimleri Enstitüsü, Adana, 109.
Carvalho, C.A., 2005. On Bruck-Reilly extensions of rectangular bands, zero semigroups and free monoids. Southeast Asian Bull. Math., 29(3), 423-431.
Carvalho, C.A. and Ruskuc, N, 2006. Finite presentability of Bruck-Reilly extensions of semilattices. Communications in Algebra, 34(9), 3301-3313.
Carvalho, C.A. and Ruskuc, N, 2007. Finite presentability of Bruck-Reilly extensions of Clifford monoids. Journal of Algebra and Its Applications, 6(5), 801-814.
Carvalho, C.A., 2009. Bruck-Reilly extensions of direct products of monoids and completely (0)-simple semigroups. Semigroup Forum, 79, 145-158.
Carvalho, C.A., 2009. On Presentations of Bruck-Reilly extensions. Communications in Algebra, 34, 2871-2886.
Çevik, A.S, 2003. Minimal but inefficient presentations of the semi-direct products of some monoids. Semigroup Forum, 66, 1-17.
Çevik, A.S, 2003. The p-Cockcroft propertyof the semi-direct products of monoids. Internat. J. Algebra Comput., 13, 1-16.
Guba, V.S. and Pride, S.J., 1996. Low dimensional (co)homology of free Burnside monoids. Journal Pure Appl. Algebra, 108, 61-79.
Howie, J. M. and Ruskuc, N., 1994. Construction and presentations for monnoids. Communications in Algebra, 22(15), 6209-6224.
Howie, J. M., 1995. Fundamentals of Semigroup Theory. New York, Oxford University Press.
Johnson, D.L., 1990. Presentations of Groups. Cambridge Univ. Press, Cambridge.
Karpuz, E. G., 2015. Gröbner-Shirshov Bases of Some Semigroup Constructions. Algebra Colloquium, 22(1), 35-46.
Yağcı, M. (2024). Monoidlerin Bruck-Reilly Genişlemelerinin İkinci Tamsayı Homolojisi. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, 24(2), 260-265. https://doi.org/10.35414/akufemubid.1343106
AMA
Yağcı M. Monoidlerin Bruck-Reilly Genişlemelerinin İkinci Tamsayı Homolojisi. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. April 2024;24(2):260-265. doi:10.35414/akufemubid.1343106
Chicago
Yağcı, Melek. “Monoidlerin Bruck-Reilly Genişlemelerinin İkinci Tamsayı Homolojisi”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 24, no. 2 (April 2024): 260-65. https://doi.org/10.35414/akufemubid.1343106.
EndNote
Yağcı M (April 1, 2024) Monoidlerin Bruck-Reilly Genişlemelerinin İkinci Tamsayı Homolojisi. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 24 2 260–265.
IEEE
M. Yağcı, “Monoidlerin Bruck-Reilly Genişlemelerinin İkinci Tamsayı Homolojisi”, Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, vol. 24, no. 2, pp. 260–265, 2024, doi: 10.35414/akufemubid.1343106.
ISNAD
Yağcı, Melek. “Monoidlerin Bruck-Reilly Genişlemelerinin İkinci Tamsayı Homolojisi”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 24/2 (April 2024), 260-265. https://doi.org/10.35414/akufemubid.1343106.
JAMA
Yağcı M. Monoidlerin Bruck-Reilly Genişlemelerinin İkinci Tamsayı Homolojisi. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. 2024;24:260–265.
MLA
Yağcı, Melek. “Monoidlerin Bruck-Reilly Genişlemelerinin İkinci Tamsayı Homolojisi”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, vol. 24, no. 2, 2024, pp. 260-5, doi:10.35414/akufemubid.1343106.
Vancouver
Yağcı M. Monoidlerin Bruck-Reilly Genişlemelerinin İkinci Tamsayı Homolojisi. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. 2024;24(2):260-5.