Cinemugam (Kollywood)

SCHOOL OF ELEMENTS Q1. A. Fill in the blanks. 1.      The formula of chloride of metal M is MCl 2 . The metal M belongs to group 2. 2.      18 group in the periodic table contains elements that are all gases at room temperature. 3.      The arrangement of elements in a group of three is known as ­ traids. 4.      The law used by Newlands to arrange elements is known as Newlands’ Octaves. 5.      The element eka – aluminum in Mendeleev’s periodic table is known as Gallium in modern periodic table. 6.      Elements showing properties of both metals and non – metals are known as metalloids. Q1. B. Match the columns. Column I Column II 1.      Sodium 2.      Cerium 3.      Sulphur 4.      Manganese a.      Lanthanide b.      Metalloid c.       Transition metal d.      Noble metal e.      Metal f.        Non – metal. Ans. Column I Column II 1.      Sodium 2.      Cerium 3.      Sulphur 4.      Manganese e. Metal a. Lanthanide f.

   Chapter-III Free module Definition : 3.1          The annihilator of an R-module M is defined as                                 Ann (M)   ={ a Є R /aM =0}. Note:3.2 i)                Ann (M) is an ideal of R. ii)              If M is cyclic and is generated by x, Ann(M)   denoted by Ann(x). Definition:3.3             M is called a faithful R - module if Ann (M) =(0) Definition:3.4              M   is called a finitely generated R –module if M =M 1 +M 2 +…….+M n where each M i is cyclic.                If M i =R x i; ,then {x 1 ,x 2 ,……., x n } is called as generating   set for   M Example:3.5              The module of polynomials over R of degree atmost n is generated by 1,X,X 2 ,……X n 1,1+X, X 2 ,…..X n is also a generating set for the same module .   The generating set is not unique. Definition:3.6        M is called a direct   sum of submodules M 1 ,M 2 ,…..,M n , if every xЄ M can be uniquely expressed as