The free object generated by a set in the category of complete L-fuzzy posets is discussed in this paper. The construction of a free complete L-fuzzy poset generated by a set is obtained, which is a generalization of ...The free object generated by a set in the category of complete L-fuzzy posets is discussed in this paper. The construction of a free complete L-fuzzy poset generated by a set is obtained, which is a generalization of the free complete lattice generated by a set.展开更多
We construct free Hom-semigroups when its unary operation is multiplicative and is an involution. Our method of construction is by bracketed words. As a consequence , we obtain free Horn-associative algebras generated...We construct free Hom-semigroups when its unary operation is multiplicative and is an involution. Our method of construction is by bracketed words. As a consequence , we obtain free Horn-associative algebras generated by a set under the same conditions for the unary operation.展开更多
A dendriform algebra defined by Loday has two binary operations that give a two-part splitting of the associativity in the sense that their sum is associative. Sim- ilar dendriform type algebras with three-part and fo...A dendriform algebra defined by Loday has two binary operations that give a two-part splitting of the associativity in the sense that their sum is associative. Sim- ilar dendriform type algebras with three-part and four-part splitting of the associativity were later obtained. These structures can also be derived from actions of suitable linear operators, such as a Rota-Baxter operator or TD operator, on an associative algebra. Mo- tivated by finding a five-part splitting of the associativity, we consider the Rota-Baxter TD （RBTD） operator, an operator combining the Rota-Baxter operator and TD oper- ator, and coming from a recent study of Rota＇s problem concerning linear operators on associative algebras. Free RBTD algebras on rooted forests are constructed. We then introduce the concept of a quinquedendriform algebra and show that its defining relations are characterized by the action of an RBTD operator, similar to the cases of dendriform and tridendriform algebras.展开更多
文摘The free object generated by a set in the category of complete L-fuzzy posets is discussed in this paper. The construction of a free complete L-fuzzy poset generated by a set is obtained, which is a generalization of the free complete lattice generated by a set.
基金This work was supported by the National Natural Science Foundation of China （Grant No. 11371178） and the National Science Foundation of US （Grant No. DMS 1001855）.
文摘We construct free Hom-semigroups when its unary operation is multiplicative and is an involution. Our method of construction is by bracketed words. As a consequence , we obtain free Horn-associative algebras generated by a set under the same conditions for the unary operation.
基金This work is supported by the National Natural Science Foundation of China （Grant No. 11371178） and the National Science Foundation of US （Grant No. DMS 1001855）. Shuyun Zhou thanks the hospitality of Rutgers University at Newark during her visit in 2012-2013.
文摘A dendriform algebra defined by Loday has two binary operations that give a two-part splitting of the associativity in the sense that their sum is associative. Sim- ilar dendriform type algebras with three-part and four-part splitting of the associativity were later obtained. These structures can also be derived from actions of suitable linear operators, such as a Rota-Baxter operator or TD operator, on an associative algebra. Mo- tivated by finding a five-part splitting of the associativity, we consider the Rota-Baxter TD （RBTD） operator, an operator combining the Rota-Baxter operator and TD oper- ator, and coming from a recent study of Rota＇s problem concerning linear operators on associative algebras. Free RBTD algebras on rooted forests are constructed. We then introduce the concept of a quinquedendriform algebra and show that its defining relations are characterized by the action of an RBTD operator, similar to the cases of dendriform and tridendriform algebras.
