Tema4
This document was uploaded by user and they confirmed that they have the permission to share it. If you are author or own the copyright of this book, please report to us by using this DMCA report form. Report DMCA
Overview
Download & View Tema4 as PDF for free.
More details
- Words: 123
- Pages: 1
4
Temˇ a
P. 4.1. Fie S := N × N, iar ∗ : S × S −→ S operat¸ia binarˇa definitˇa prin (i, j) ∗ (k, l) = (i + k, j · 2k + l) . Studiat¸i dacˇ a operat¸ia ∗ este comutativˇ a, resp. asociativˇa, resp. cu element neutru. P. 4.2. Fie (M, ·, 1) un monoid, iar a, b ∈ M . Arˇatat¸i cˇa a) a ∈ U (M ) dacˇ a ¸si numai dacˇ a funct¸iile λa : M −→ M : x 7−→ ax ¸si ρa : M −→ M : x 7−→ xa sunt bijective. b) Dacˇ a M este finitˇ a, iar ab ∈ U (M ), atunci a, b ∈ U (M ).
1
Temˇ a
P. 4.1. Fie S := N × N, iar ∗ : S × S −→ S operat¸ia binarˇa definitˇa prin (i, j) ∗ (k, l) = (i + k, j · 2k + l) . Studiat¸i dacˇ a operat¸ia ∗ este comutativˇ a, resp. asociativˇa, resp. cu element neutru. P. 4.2. Fie (M, ·, 1) un monoid, iar a, b ∈ M . Arˇatat¸i cˇa a) a ∈ U (M ) dacˇ a ¸si numai dacˇ a funct¸iile λa : M −→ M : x 7−→ ax ¸si ρa : M −→ M : x 7−→ xa sunt bijective. b) Dacˇ a M este finitˇ a, iar ab ∈ U (M ), atunci a, b ∈ U (M ).
1
