tailieunhanh - Báo cáo toán học: "Regularity and Isomorphism Theorems of Generalized Order - Preserving Transformation Semigroups"

Trình tự bảo quản đầy đủ chuyển đổi nửa nhóm OT (X) trên X poset từ lâu đã được nghiên cứu. Trong bài báo này, chúng ta nghiên cứu các-nửa nhóm (OT (X, Y), θ) trong đó X và Y là chuỗi, OT (X, Y) là tập hợp của tất cả các bản đồ để bảo quản từ X vào Y, θ ∈ OT (Y , X) và hoạt động. | Vietnam Journal of Mathematics 33 3 2005 253-260 V Í e It ini ai m J o mt r im ai I of MATHEMATICS VAST 2005 Regularity and Isomorphism Theorems of Generalized Order - Preserving Transformation Semigroups Yupaporn Kemprasit1 and Sawian Jaidee2 1 Department of Mathematics Faculty of Science Chulalongkorn University Bangkok 10330 Thailand 2 Department of Mathematics Faculty of Science Khon Kean Univeisily Khon Kean 40002 Thailand Received April 15 2003 Revised June 6 2005 Abstract. The full order-preserving transformation a poset has long been studied. In this paper we study the semigroup. where and are chains .is the set of all order-preserving maps from into .and the operation is defined all .We characterize regular . .and. . 1. Introduction . .1 2 1 order--isomorphism . .order-preserving 2 1 2 A 1 . order-isomorphic. .anti order isomorphic. .1 2 1 2 2 1 254 Yupaporn Kemprasit and Sawian Jaidee . . . . .full order-preserving transformation semigroup . Z R . . .Z .R. Theorem For any nonempty subset of Z .is regular. Theorem For a nonempty interval of R .is regular if and only if is closed and bounded. . .X. X. 2. Lemmas Lemma . Let a b and. be such . defined by . . . . then. Proof. . Lemma . regular then is one to one. Proof. . . Regularity and Isomorphism Theorems 255 Lemma . an identity n then is one-to-one and ran . .y. . _ y y . . . y y .Y. . Lemma . Let e f be such that and . If. for defined by . . . . . . If. for defined by . . . . Proof. Lemma . . . for some. is regular then for every. Proof. . . Case 1. . . . Case .