Skew linear groups by M Shirvani; Bertram A F Wehrfritz

By M Shirvani; Bertram A F Wehrfritz

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Extra resources for Skew linear groups

Example text

If W = V then the n-n set linear transformation is defined to be a n-n set linear operator on V. 28: Let °­§ m  mI 0 · °½  V = ®¨ ¸ m  Z  ^0`¾ 0¹ ¯°© 0 ¿° and W = {m – mI | m  Z+  {0}} be two n-n set linear algebras over the set S = {0, 1, 1 – I}  N(Z). Define T: V o W by § m  mI 0 · T¨ ¸ = 2m – 2mI 0¹ © 0 for every § m  mI 0 · ¨ ¸ V 0¹ © 0 and T(0) = 0. Thus T is a n-n set linear transformation of V into W. 29: Let V = {2ZI} and ½° 0 · °­§ 2ZI  W = ®¨ ¸ m  Z  ^0`¾ ¯°© 0 m  mI ¹ ¿° be two n-n set linear algebras over the set S = {0, 1, 1 – I}  N(Z).

T = {2nI | n  Z \ 36 {0}}  V is the pure neutrosophic integer set generator of V over S = {0, 1}. 61: Let V = {2I, 9I, –8I, 14I, 27I + 4, 44 – 2I, 0, 14I – 9}  PN(Z) be a pure neutrosophic integer set vector space with zero over S = {0,1}  Z. , V \ {0} = T is the pure neutrosophic integer set generator of V over S. 62: Let V = {3ZI} be the pure neutrosophic integer set vector space over the set S = Z. T = {3}  V is the pure neutrosophic integer set generator of V over S = Z. Thus | T | = 1.

It is important and interesting to note that as in case of linear algebra, n-n linear algebras is a set vector space but in general a n-n set vector space is not a n-n linear algebra. The following examples show that a n-n set vector space is not a n-n set linear algebra. 12: Let V = {3I, 24I, 41I, 26I, 0, –13I, 48I}  PN(Z). V is a n-n set vector space over the set S = {0, 1, I}  N(Z). We see V is not a n-n set linear algebra over S; as 3I + 24I = 27I  V and so on. Thus in general a n-n set vector space is not a n-n set linear algebra over S.