# Algebraic geometry over algebraic structures. II. Foundations

## Related Articles

- A unified theory of generalized closed sets in weak structures. Al-Omari, Ahmad; Noiri, Takashi // Acta Mathematica Hungarica;Apr2012, Vol. 135 Issue 1/2, p174
A new kind of sets called generalized w-closed (briefly gw-closed) sets is introduced and studied in a topological space by using the concept of weak structures introduced by Ã. CsÃ¡szÃ¡r in [6]. The class of all gw-closed sets is strictly larger than the class of all w-closed sets....

- Representations of Ariki?Koike algebras and Grï¿½bner?Shirshov bases The research of the first author was supported by KOSEF Grant # 98-0701-01-5-L and the Young Scientist Award, Korean Academy of Science and Technology. The... Kang, Seok-Jin; Lee, In-Sok; Lee, Kyu-Hwan; Oh, Hyekyung // Proceedings of the London Mathematical Society;Jul2004, Vol. 89 Issue 1, p54
In this paper, we investigate the structure of Ariki?Koike algebras and their Specht modules using Grï¿½bner?Shirshov basis theory and combinatorics of Young tableaux. For a multipartition $\lambda$, we find a presentation of the Specht module $S^{\lambda}$ given by generators...

- Algebraic structures within subsets of Hamel and SierpiÅ„nski-Zygmund functions. Płotka, Krzysztof // Bulletin of the Belgian Mathematical Society - Simon Stevin;Aug2015, Vol. 22 Issue 3, p447
We prove the existence of an additive semigroup of cardinality 2c contained in the intersection of the classes of Hamel functions (HF) and SierpiÅ„ski-Zygmund functions (SZ). In addition, we show that under certain set-theoretic assumptions the lineability of the class of...

- DERIVATIONS OF THE 3-LIE ALGEBRA REALIZED BY gl (n, C). RUIPU BAI; JINXIU WANG; ZHENHENG LI // Journal of Nonlinear Mathematical Physics (World Scientific Publ;Mar2011, Vol. 18 Issue 1, p151
This paper studies structures of the 3-Lie algebra realized by the general linear Lie algebra M gl(n, C). We show that has only one nonzero proper ideal. We then give explicit expressions of n, M both derivations and inner derivations of . Finally, we investigate substructures of the (inner) M...

- Analysis of functions that are hierarchical as algebraic structures. Akhobadze, M.; Zumburidze, O. // Journal of Mathematical Sciences;Nov2012, Vol. 186 Issue 5, p683
The mathematical analysis of a connection can be implemented according to different approaches in order to characterize the system structure R.

- Noncommutative semialgebraic sets in nilpotent variables. Loring, Terry A.; Shulman, Tatiana // New York Journal of Mathematics;2012, Vol. 18, p361
We solve the lifting problem in C*-algebras for many sets of relations that include the relations Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed. for all variables. The remaining relations must be of the form |p(x1,â€¦xn)| â‰¤ C for C a...

- The computable embedding problem. Carson, J.; Fokina, E.; Harizanov, V.; Knight, J.; Quinn, S.; Safranski, C.; Wallbaum, J. // Algebra & Logic;Jan2012, Vol. 50 Issue 6, p478
Calvert calculated the complexity of the computable isomorphism problem for a number of familiar classes of structures. Rosendal suggested that it might be interesting to do the same for the computable embedding problem. By the computable isomorphism problem and (computable embedding problem) we...

- Introduction to Bihypergroups. Davvaz, B.; Agboola, A. A. A. // International Journal of Mathematical Combinatorics;Jun2013, Vol. 2, p54
Similar to groups, the union of two sub-hypergroups do not form a hypergroup but they find a nice hyperstructure called bihypergroup. This short note is devoted to the introduction of bihypergroups and illustrate them with examples. A characterization theorem about sub-bihypergroups is given and...

- On Mathematical Modelling of Time-Related Musical Structures. Albrecht, I. // Journal of Mathematical Sciences;Sep2013, Vol. 193 Issue 3, p341
In this article, the first steps towards mathematical modelling of time-related musical structures are taken, and the algebraic structure of musical time relations is elaborated starting from a perceptive point of view. A basic characterization of fundamental properties of perceived time...